DSpace Community: KAIST Dept. of Mathematical Sciences
KAIST Dept. of Mathematical Sciences
http://hdl.handle.net/10203/527
2022-05-21T00:35:30Z
2022-05-21T00:35:30Z
Bayesian mixture of gaussian processes for data association problem
Jeon, Younghwan
Hwang, Ganguk
http://hdl.handle.net/10203/295865
2022-04-25T06:00:10Z
2022-07-01T00:00:00Z
Title: Bayesian mixture of gaussian processes for data association problem
Authors: Jeon, Younghwan; Hwang, Ganguk
Abstract: We address the data association problem and propose a Bayesian approach based on a mixture of Gaus-sian Processes (GPs) having two key components, the assignment probabilities and the GPs. In the pro-posed approach, the two key components are simultaneously updated according to observations through an efficient Expectation-Maximization (EM) algorithm that we develop. The proposed approach is thus more adaptive to the observations than the existing approaches for data association. To validate the per-formance of the proposed approach, we provide experimental results with real data sets as well as two synthetic data sets. We also provide a theoretical analysis to show the effectiveness of the Bayesian up -date.(c) 2022 Elsevier Ltd. All rights reserved.
2022-07-01T00:00:00Z
Obstructions for partitioning into forests and outerplanar graphs
Kim, Ringi
Norin, Sergey
Oum, Sang-il
http://hdl.handle.net/10203/292543
2022-04-13T06:46:09Z
2022-05-01T00:00:00Z
Title: Obstructions for partitioning into forests and outerplanar graphs
Authors: Kim, Ringi; Norin, Sergey; Oum, Sang-il
Abstract: For a class C of graphs, we define C-edge-brittleness of a graph G as the minimum ℓ such that the vertex set of G can be partitioned into sets inducing a subgraph in C and there are ℓ edges having ends in distinct parts. We characterize classes of graphs having bounded C-edge-brittleness for a class C of forests or a class C of graphs with no K4∖e topological minors in terms of forbidden obstructions. We also define C-vertex-brittleness of a graph G as the minimum ℓ such that the edge set of G can be partitioned into sets inducing a subgraph in C and there are ℓ vertices incident with edges in distinct parts. We characterize classes of graphs having bounded C-vertex-brittleness for a class C of forests or a class C of outerplanar graphs in terms of forbidden obstructions. We also investigate the relations between the new parameters and the edit distance. © 2020 The Author(s)
2022-05-01T00:00:00Z
The relative Whitney trick and its applications
Davis, Christopher W.
Orson, Patrick
Park, JungHwan
http://hdl.handle.net/10203/291698
2022-04-21T11:01:10Z
2022-05-01T00:00:00Z
Title: The relative Whitney trick and its applications
Authors: Davis, Christopher W.; Orson, Patrick; Park, JungHwan
Abstract: We introduce a geometric operation, which we call the relative Whitney trick, that removes a single double point between properly immersed surfaces in a 4-manifold with boundary.Using the relative Whitney trick we prove that every link in a homology sphere is homotopic to a link that is topologically slice in a contractible topological 4-manifold. We further prove that any link in a homology sphere is order k Whitney tower concordant to a link in S-3 for all k. Finally, we explore the minimum Gordian distance from a link in S-3 to a homotopically trivial link. Extending this notion to links in homology spheres, we use the relative Whitney trick to make explicit computations for 3-component links and establish bounds in general.
2022-05-01T00:00:00Z
On the first Steklov-Dirichlet eigenvalue for eccentric annuli
Hong, Jiho
Lim, Mikyoung
Seo, Dong-Hwi
http://hdl.handle.net/10203/292580
2022-04-21T11:02:39Z
2022-04-01T00:00:00Z
Title: On the first Steklov-Dirichlet eigenvalue for eccentric annuli
Authors: Hong, Jiho; Lim, Mikyoung; Seo, Dong-Hwi
Abstract: In this paper, we investigate the first Steklov-Dirichlet eigenvalue on eccentric annuli. The main geometric parameter is the distance t between the centers of the inner and outer boundaries of an annulus. We first show the differentiability of the eigenvalue in t and obtain an integral expression for the derivative value in two and higher dimensions. We then derive an upper bound of the eigenvalue for each t, in two dimensions, by the variational formulation. We also obtain a lower bound of the eigenvalue, given a restriction that the two boundaries of the annulus are sufficiently close. The key point of the proof of the lower bound is in analyzing the limit behavior of an infinite series expansion of the first eigenfunction in bipolar coordinates. We also derive a relation between the first eigenvalue and a sequence of eigenvalues obtained by a finite section method. Based on this relation, we also perform numerical experiments that exhibit the monotonicity for two dimensions.
2022-04-01T00:00:00Z