[2019 Spring Semester]
매주 화요일 12:00
운영위원 : 장현태 ( a24325@ajou.ac.kr , 팔달관 622호 )
감독위원 : 문지연 ( j9746@ajou.ac.kr , 팔달관 622호 )
Title : A comparison of imputation methods for missing data
Abstract : Many existing industrial and research data sets contain missing values due to various reasons. The important factors for selection of approach to missing values is missing data mechanism. Many imputation methods have been proposed according to character of data and mechanism of missingness. In this study, we apply several imputation methods assumed on various distributions though simulation. And we suggest the optimal imputation methods according to distributions.
Title : Outer detection and treatment in sample survey
Abstract : 통상적으로 왜도가 심한 분포를 따르는 표본조사를 이용하여 모집단의 총계를 추정함에 있어서 이상치(outlier)는 큰 영향을 준다. 뿐만 아니라 관측치의 가중치(weight)가 크거나 혹은 미미한 경우 역시 총계를 추정함에 영향을 줄 수 있다. 특히 부동산 혹은 사업체 등등에서는 왜도가 심하여 꼬리가 긴 분포의 형태로 나타나는 경우가 일반적이므로 이상치는 총계를 추정함에 있어서 과대 혹은 과소평가 시키는 문제를 야기한다. 하지만 통계학 분야에서 연구된 이상치에 관한 내용들은 실무에서의 표본자료들에 관해선 연구가 미비한 상태일 뿐만 아니라 해당 방법론을 적용시키기에 무리가 있다. 이러한 문제를 해결해 보고자 본 연구에서는 실제로 조사된 부동산 자료에서 네이만 배분법(Neyman allocation method)을 이용해 표본을 추출하여 이상치 판별을 위해 다양한 방법들을 제시 후 윈저화(Winsorization) 방법, 가중치 조정함수를 통한 가중치 조정 방법 및 기존의 네이만 배분법의 총계 추정방법을 적용 후 총계를 추정하여 그 결과를 살펴보고 보다 합리적인 방법론을 제안하고자 한다.
Title : Sturmian shifts
Abstract : In this talk we are going to discuss about Circle rotations, Sturmian words. Give some equivalent conditions between circle rotations and Sturmian words.
Title : On Brauer groups of toric log del Pezzo surfaces
Abstract : If S is a normal toric surface, then it is known that the cohomological Brauer group Br(S) is computable. In particular, if S is projective, then we compute Br(S) is isomorphic to for some cyclic group. Since toric log del Pezzo surface is projective toric surface, and has 1-1 correspondence to Fano polygon, we can compute Br(S) by Fano polygon.
Title : Symbolic representation
Abstract : In this talk, we define generators and introduce how to induce a symbolic dynamical system from a given dynamical system.
Title : A generalization of real toric manifolds
Abstract : A real Lagrangian submanifold of a symplectic toric manifold $M$ is given by the fixed point set of an anti-symplectic involution on it. If the involution is standard, then the real Lagrangian is a real toric manifold. To obtain nontrivial anti-symplectic involutions, we shall lift a symmetry of the Delzant polytope of $M$ to an anti-symplectic involution on $M$. This will be useful to study the topology of real Lagrangians. This is an ongoing project with Joe Brendel and Joontae Kim.
Title : Digraphs, Markov chain and shifts of finite type
Abstract : In this talk we are going to discuss about Shift of finite type, Digraphs. And introduce how to construct edge/vertex shift, the relationship between edge shift and vertex shift.
Title : Oriented colorings of graphs with small maximum degree
Abstract : An oriented graph is a digraph obtained from a simple, undirected graph by assigning to each edge one of two possible orientations. An oriented k-coloring of an oriented graph G is a function c : V(G)→{0, 1, … , k-1} such that c(u)≠c(v) for all uv∈E(G), and for all uv, xy∈E(G), if c(u)=c(y), then c(v) ≠c(x). In this talk we review the paper on oriented colorings of graph with maximum degree three and four. The results are any orientation of a graph with maximum degree three and four have an oriented 9-coloring, and oriented 69-coloring, respectively.
Title : Elliptic Curve Cryptography
Abstract : In this talk, we define elliptic curves as groups, and discuss about public key cryptography and Elliptic Curve Cryptography (ECC).