[2018 Spring Semester]
매주 수요일 12:00
운영위원 : 강성식 ( matherr@ajou.ac.kr , 팔달관 622호 )
감독위원 : 문지연 ( j9746@ajou.ac.kr , 팔달관 622호 )
Title : Projective toric manifolds over wedges of a 3-cube with one vetex cut
Abstract : The wedge operation is a classical operation defined on the set of simplicial complexes. We completely classify toric manifolds over simplicial complexes obtained by a sequence of wedges from the dual complex of 3-cube with one vertex cut. Using the Shephard's diagram, We also verify that whether all of them are projective or not. This talk is based on joint with Suyoung Choi and Hanchul Park.
Title : On incidence choosability of cubic graphs
Abstract : An incidence of a graph G is a pair (v; e) where v is a vertex of G and e is an edge of G incident with v. Two incidences (u; e) and (v; f) of G are adjacent whenever (i) u = v, or (ii) e = f, or (iii) uv = e or uv = f. An incidence k-coloring of G is a mapping from the set of incidences of G to a set of k colors such that every two adjacent incidences receive distinct colors. The notion of incidence coloring has been introduced by Brualdi and Quinn Massey (1993) from a relation to strong edge coloring, and since then, attracted by many authors. On a list version of incidence coloring, it was shown by Benmedjdoub et. al. (2017) that every Hamiltonian cubic graph is incidence 6-choosable. In this paper, we show that every cubic (loopless) multigraph is incidence 6-choosable. As a direct consequence, it implies that the list strong chromatic index of a (2; 3)-bipartite graph is at most 6, where a (2,3)-bipartite graph is a bipartite graph such that one partite set has maximum degree 2 and the other part has maximum degree 3.
Title : Open maps between shift spaces
Abstract : Given a code from a shift space to an irreducible sofic shift, any two of the three conditions- open, constant-to-one and closing -- imply the third. If the range is not sofic, then the same result holds when bi-closingness replaces closingness. properties of open mappings between shift spaces are investigated in detail. In particular, we show that a closing open(or constant-to-one) extension preserves the structure of a sofic shift.
Title : Several Imputation methods for longitudinal data
Abstract : Longitudinal studies play an important role in scientific researches. The defining characteristic of the longitudinal studies is that observations are collected from each subject repeatedly over time, or under different conditions. Missing values are common in longitudinal studies. The presence of missing values is always a fundamental challenge since it produces potential bias, even in well controlled conditions. Three different missing data mechanisms are defined(MCAR, MAR, MNAR). Several imputation methods have been developed in literature to handle missing values in longitudinal data. The most commonly used imputation methods include complete case analysis (CCA), mean imputation (Mean), last observation carried forward (LOCF), hot deck (HOT), regression imputation (Regress), K-nearest neighbor (KNN), The expectation maximization (EM) algorithm, and multiple imputation (MI).