• Journal of applied mathematics & informatics
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• v.42 no.4
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• pp.985-995
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• 2024

We see fundamental properties of the log-determinant α-divergence including the convexity of weighted geometric mean and the reversed sub-additivity under tensor product. We introduce a symmetrized divergence and show its properties including the boundedness and monotonicity on parameters. Finally, we discuss the barycenter minimizing the weighted sum of symmetrized divergences.

• Journal of Institute of Control, Robotics and Systems
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• v.21 no.7
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• pp.677-683
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• 2015

This paper proposes a helicopter direction adjustment system using barycenter shift. Most conventional methods for direction adjustment of uniaxial helicopters rely on the angle of inclination of the main rotor. However, the inherent burden of the bearing of the main rotor and serious abrasion of the helicopter using the above methods may results in loss of balance. To decrease abrasion and enhance the barycenter stability, the proposed method was used to shift the barycenter of the helicopter instead of the main rotor for direction adjustment. We set a biaxial ARM on a uniaxial helicopter to adjust the direction of ARM pointing as well as to realize stable direction control when the helicopter loses its balance. The method may enhance the landing safety of helicopters in emergencies. Uniaxial helicopters can be controlled under any environment by adjusting the motor parameters of the ARM which is dependent on the center of mass using neural network. The experiment results show that the helicopter can return to the starting position quickly under the external disturbance.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.371-384
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• 2022

Fix an integer n ≥ 1. Then the simplex Π_n, Birkhoff polytope Ω_n, and Latin square polytope Λ_n each yield projective geometries obtained by identifying antipodal points on a sphere bounding a ball centered at the barycenter of the polytope. We investigate conditions for homogeneous coordinates of points in the projective geometries to locate exact vertices of the respective polytopes, namely crisp distributions, permutation matrices, and quasigroups or Latin squares respectively. In the latter case, the homogeneous conditions form a crucial part of a recent projective-geometrical approach to the study of orthogonality of Latin squares. Coordinates based on the barycenter of Ω_n are also suited to the analysis of generalized doubly stochastic matrices, observing that orthogonal matrices of this type form a subgroup of the orthogonal group.

• Journal of the Korean Mathematical Society
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• v.44 no.5
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• pp.1051-1063
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• 2007

The aim of this note is to advertise a method which turns out to be powerful enough to be used successfully in problems which are apparently unrelated. It is based on a modification of a construction that we first introduced in [2].

• Journal of the Korean Mathematical Society
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• v.59 no.3
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• pp.549-570
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• 2022

In this paper, we study the Birkhoff's ergodic theorem on geodesic metric spaces, especially on Hadamard spaces, using the notion of weighted inductive means. Also, we study a deterministic weighted sequence for the weighted Birkhoff's ergodic theorem in Hadamard spaces.

• Proceedings of the Korean Society for Bioinformatics Conference
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• 2003.10a
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• pp.26-51
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• 2003

Large scale protein interaction maps provide a new, global perspective with which to analyse protein function. PSIMAP, the Protein Structural Interactome Map, is a database of all the structurally observed interactions between superfamilies of protein domains with known three-dimensional structure in thePDB. PSIMAP incorporates both functional and evolutionary information into a single network. It makes it possible to age protein domains in terms of taxonomic diversity, interaction and function. One consequence of it is to predict the most important protein domain structure in evolution. We present a global analysis of PSIMAP using several distinct network measures relating to centrality, interactivity, fault-tolerance, and taxonomic diversity. We found the following results: ${\bullet}$ Centrality: we show that the center and barycenter of PSIMAP do not coincide, and that the superfamilies forming the barycenter relate to very general functions, while those constituting the center relate to enzymatic activity. ${\bullet}$ Interactivity: we identify the P-loop and immunoglobulin superfamilies as the most highly interactive. We successfully use connectivity and cluster index, which characterise the connectivity of a superfamily's neighbourhood, to discover superfamilies of complex I and II. This is particularly significant as the structure of complex I is not yet solved. ${\bullet}$ Taxonomic diversity: we found that highly interactive superfamilies are in general taxonomically very diverse and are thus amongst the oldest. This led to the prediction of the oldest and most important protein domain in evolution of lift. ${\bullet}$ Fault-tolerance: we found that the network is very robust as for the majority of superfamilies removal from the network will not break up the network. Overall, we can single out the P-loop containing nucleotide triphosphate hydrolases superfamily as it is the most highly connected and has the highest taxonomic diversity. In addition, this superfamily has the highest interaction rank, is the barycenter of the network (it has the shortest average path to every other superfamily in the network), and is an articulation vertex, whose removal will disconnect the network. More generally, we conclude that the graph-theoretic and taxonomic analysis of PSIMAP is an important step towards the understanding of protein function and could be an important tool for tracing the evolution of life at the molecular level.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.1
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• pp.65-71
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• 2009

Let f be an 2-isometry on a non-Archimedean 2-normed space. In this paper, we prove that the barycenter of triangle is invariant for f up to the translation by f(0), in this case, needless to say, we can imply naturally the Mazur-Ulam theorem in non-Archimedean 2-normed spaces.

• Nonlinear Functional Analysis and Applications
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• v.26 no.4
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• pp.649-662
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• 2021

Recently the author studied a one-parameter family of divergences and considered the related median minimization problem of finite points over these divergences in general symmetric cones. In this article, to utilize the results practically, we deal with a special symmetric cone called second order cone, which is important in optimization fields. To be more specific, concrete computations of divergences with its gradients and the unique minimizer of the median minimization problem of two points are provided skillfully.

• Journal of Information Processing Systems
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• v.14 no.2
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• pp.435-447
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• 2018

Fingerprint-based biometric identification is one of the most interesting automatic systems for identifying individuals. Owing to the poor sensing environment and poor quality of skin, biometrics remains a challenging problem. The main contribution of this paper is to propose a new approach to recognizing a person's fingerprint using the fingerprint's local characteristics. The proposed approach introduces the barycenter notion applied to triangles formed by the Delaunay triangulation once the extraction of minutiae is achieved. This ensures the exact location of similar triangles generated by the Delaunay triangulation in the recognition process. The results of an experiment conducted on a challenging public database (i.e., FVC2004) show significant improvement with regard to fingerprint identification compared to simple Delaunay triangulation, and the obtained results are very encouraging.

• International Journal of CAD/CAM
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• v.6 no.1
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• pp.89-97
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• 2006

This paper presents a novel approach for non-iterative surface smoothing with feature preservation on arbitrary meshes. Laplacian operator is performed in a global way over the mesh. The surface smoothing is formulated as a quadratic optimization problem, which is easily solved by a sparse linear system. The cost function to be optimized penalizes deviations from the global Laplacian operator while maintaining the overall shape of the original mesh. The features of the original mesh can be preserved by adding feature constraints and barycenter constraints in the system. Our approach is simple and fast, and does not cause surface shrinkage and distortion. Many experimental results are presented to show the applicability and flexibility of the approach.