Variational Models and Fast Numerical Schemes in Image Profcessing and Computer Vision Lecture 2

● Mathematical preliminaries

● Image restoration, inpainting and Deblurring

● Fast numerical schemes

● Image segmentation and geometrical PDEs

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Inquiry: Prof. Chang-Ock Lee()

Variational Models and Fast Numerical Schemes in Image Profcessing and Computer Vision Lecture 1

● Mathematical preliminaries

● Image restoration, inpainting and Deblurring

● Fast numerical schemes

● Image segmentation and geometrical PDEs

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Inquiry: Prof. Chang-Ock Lee()

삼성전자 반도체 사업부 세미나

 

YE팀(Yield Enhancement Team)은 반도체공정에 대한 Metrology & Inspection 기술 개발 및 적용을 담당하는 부서로 Nanometer 영역에 대한 최첨단 기술개발에 도전하고자 하는 능력 있는 우수인재들과 새로운 미래를 열어가고자 합니다.

 

▶ 세미나 요약  : 반도체 제작 공정에는 수백 개의 계측, 검사 공정이 포함되어 있으며 제작 공정 난이도 증가에 따라 계측 공정의 중요성도 점차 커지고 있습니다. 계측 기술이라 함은  다양한 광학, eBeam, X-ray 등의 source로부터 얻어진 data를 가공하여 원하는 정보를 추출하는 작업이며, 이에 Image processing, Data mining, Electro-magnetic simulation 등의 다양한 수학적 기술이 필요합니다.

본 세미나에서는 이와 같은 다양한 필요 기술을 소개하고자 합니다.

 

▶ 주요기술 

  - Simulation Technique (FDTD, RCWA, Monte Carlo Simulation)

  - Image processing  (Segmentation, Inspection)

  - Data mining (Classification, Clustering, Feature extraction)

  - Optics System Design (Microscopy, Ellipsometer, Interferometer)

  - Mechanical System Design (Stage Control, System Noise Analysis)

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세미나 후 별도의 취학 상담도 진행 하오니 관심 있는 학생분들의 많은 참여 바랍니다

Recently, Kenyon and Wilson introduced a certain matrix M in order to compute
pairing probabilities of what they call the double-dimer model. They showed that the absolute value of each entry of the inverse matrix M^-1 is equal to the number of certain Dyck tilings of
a skew shape. They conjectured two formulas on the sum of the absolute values of the entries in a row or a column of M^-1. In this talk we prove the two conjectures. As a consequence
we obtain that the sum of the absolute values of all entries of M^-1 is equal to the number of
complete matchings. We also find a bijection between Dyck tilings and complete matchings.

This talk is based on the following paper: arxiv:1108.5558.

Magnetic resonance electrical impedance tomography (MREIT) aims to visualize a conductivity distribution inside the human body. When we apply the harmonic Bz algorithm to measured Bz data from animal or human subjects, there occur a few technical difficulties that are mainly related with measurement errors in Bz data especially in a local region where MR signals are very small. We investigate sources of the error and its adverse effects on the image reconstruction process. We suggest a new error propagation blocking algorithm to prevent defective data at one local region from influencing badly on conductivity images of other regions. We experimentally examine the performance of the proposed method by comparing reconstructed images with and without applying the error propagation blocking algorithm.

We present an approximate converse theorem which measures how close a given set of irreducible admissible unramified unitary generic local representations of GL(n) is to a genuine cuspidal representation. To get a formula for the measure, we introduce a quasi-Maass form on the generalized upper half plane for a given set of local representations. We also construct an annihilating operator which enables us to write down an explicit cuspidal automorphic function.

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7월 6일~8월 31일 매주금요일

In this talk, we introduce a novel gauge construction for the Yang-Mills equations on the Minkowski space $bbR^{1+3}$, utilizing the properties of the associated Yang-Mills heat flow in a crucial way. The idea of constructing a gauge using the associated geometric heat flow, which goes under the name emph{caloric} gauge, was first proposed by Tao ('04) in the context of energy-critical wave maps and further developed by Bejenaru-Ionescu-Kenig-Tataru ('11) and Smith ('11) for energy-critical Schr"odinger maps. The novel gauge for the Yang-Mills equations is seen to possess a number of desirable properties; in particular, it does not have any issues with `large' data, in contrast with the classical Coulomb gauge. As the first demonstration of the structure offered by this new gauge, we will give an alternative proof of the global existence of solutions with finite energy to the Yang-Mills equation, a result first proved by Klainerman-Machedon ('95) using local Coulomb gauges.

An old problem raised independently by Jacobson and Schönheim asks to determine the maximum s for which every graph with m edges contains a pair of edge-disjoint isomorphic subgraphs with s edges. We determine this maximum up to a constant factor and show that every m-edge graph contains a pair of edge-disjoint isomorphic subgraphs with at least c (m log m)2/3 edges for some absolute constant c, and find graphs where this estimate is off only by a multiplicative constant. Our results improve bounds of Erdős, Pach, and Pyber from 1987. Joint work with Po-Shen Loh and Benny Sudakov.

A dynamic coloring of a graph G is a proper coloring of the vertex set V(G) such that for each vertex of degree at least 2, its neighbors receive at least two distinct colors. A  dynamic k-coloring of a graph is a dynamic coloring with k colors. Note that the gap χ_d(G) – χ(G) could be arbitrarily large for some graphs. An interesting problem is to study which graphs have small values of χ_d(G) – χ(G).
One of the most interesting problems about dynamic chromatic numbers is to find upper bounds of χ_d(G)$  for planar graphs G. Lin and Zhao (2010) and Fan, Lai, and Chen (recently) showed that for every planar graph G, we have χ_d(G)≤5, and it was conjectured that χ_d(G)≤4 if G is a planar graph other than C₅. (Note that χ_d(C₅)=5.)
As a partial answer, Meng, Miao, Su, and Li (2006)  showed that the dynamic chromatic number of Pseudo-Halin graphs, which are planar graphs, are at most 4, and Kim and Park (2011) showed that χ_d(G)≤4 if G is a planar graph with girth at least 7.
In this talk we settle the above conjecture that χ_d≤4 if G is a planar graph other than C₅. We also study the corresponding list coloring called a list dynamic coloring.
This is joint work with Seog-Jin Kim and Won-Jin Park.

글로벌 금융위기 및 최근 미국과 유럽의 재정위기 이후 파생상품에 대한 부정적 인식이 증가하고 있다. 장외 파생상품 및 파생결합증권의 규제강화로 상대적으로 장내파생상품 시장이 비중이 증가하고 있으나, 파생상품 전체적으로는 성장세가 둔화되고 있다. 본 보고서에서는 장내 및 장외파생상품, 그리고 최근 급격히 증가하고 있는 파생결합증권의 최근 동향 및 위험요인을 살펴본다. 신용위험(credit risk), 거래상대방 위험(counter-party risk), 극단적 상황에서의 손실 위험(extreme-event risk) 등 파생상품의 위험요인과 관련해서 금융투자회사의 위험관리의 개선과제를 제시한다. 또한 금융혁신(financial innovation), 위험분산(risk sharing), 가격발견(price discovery) 기능 등 파생상품의 순기능을 재점검해본다.

A description of the product structure of the cohomology of polyhedral products is given in terms of the stable splitting. Several applications will be discussed. This report is based on joint work with Martin Bendersky, Fred Cohen and Sam Gitler.

This survey talk will be a review results obtained in collaboration with Mattias Franz and Nigel Ray. As singular toric varieties, weighted projective spaces have an action of a real torus. The equivariant cohomology with respect to this action is computed to be isomorphic to the ring of piecewise polynomials on the defining fan. The theory is seen to parallel that for smooth toric varieties with the role of the Stanley-Reisner ring replaced by the ring of piecewise polynomials. If time permits, an alternative presentation of weighted projective spaces as iterated Thom complexes will be discussed briefly. Further collaboration with Mattias Franz, Nigel Ray and Dietrich Notbohm yields in a complete topological classification of weighted projective spaces.

Certain natural subspaces of a product of CW complexes, called polyhedral products, play an important role in a variety of different fields including: toric varieties, toric manifolds/orbifolds, intersections of quadrics, homotopy theory, algebraic combinatorics complements of subspace arrangements, robotics and group theory. The talk will survey certain combinatorics based constructions on polyhedral products which allow for a description of the cohomology rings of certain families of toric manifolds in a particularly compact form. The new constructions will be related to a generalization of the basic Davis-Januszkiewicz construction of toric manifolds. This report is based on joint work with Martin Bendersky, Fred Cohen and Sam Gitler.

본 강연은 KMRS(KIAST Math Research Station)에서 제공하는 집중 강연으로 기하학적 입장에서 유도되어지는 편미분 방정식을 소개하는 것을 목적으로 하고 있다. 이제까지 주로 연구 되어진 다양한 편미분 방정식은 주로 물리학적인 문제들에서 유도 되어진 것이다. 본 강연을 통해서 기존의 편미분 방정식을 보다 기하학적인 관점에서 이해할 뿐 아니라 기하학적인 문제를 편미분 방정식의 형태로 소개 하고자 한다.   This lecture series is provided by KMRS and aiming to introduce PDEs which are derived from geometry view point. So far PDEs are mostly derived from physical view point. In these lectures PDEs will be understood in geometry view point and PDEs related to geometry will be introduced.

본 강연은 KMRS(KIAST Math Research Station)에서 제공하는 집중 강연으로 기하학적 입장에서 유도되어지는 편미분 방정식을 소개하는 것을 목적으로 하고 있다. 이제까지 주로 연구 되어진 다양한 편미분 방정식은 주로 물리학적인 문제들에서 유도 되어진 것이다. 본 강연을 통해서 기존의 편미분 방정식을 보다 기하학적인 관점에서 이해할 뿐 아니라 기하학적인 문제를 편미분 방정식의 형태로 소개 하고자 한다.  

This lecture series is provided by KMRS and aiming to introduce PDEs which are derived from geometry view point. So far PDEs are mostly derived from physical view point. In these lectures PDEs will be understood in geometry view point and PDEs related to geometry will be introduced.

본 강연은 KMRS(KIAST Math Research Station)에서 제공하는 집중 강연으로 기하학적 입장에서 유도되어지는 편미분 방정식을 소개하는 것을 목적으로 하고 있다. 이제까지 주로 연구 되어진 다양한 편미분 방정식은 주로 물리학적인 문제들에서 유도 되어진 것이다. 본 강연을 통해서 기존의 편미분 방정식을 보다 기하학적인 관점에서 이해할 뿐 아니라 기하학적인 문제를 편미분 방정식의 형태로 소개 하고자 한다.  

This lecture series is provided by KMRS and aiming to introduce PDEs which are derived from geometry view point. So far PDEs are mostly derived from physical view point. In these lectures PDEs will be understood in geometry view point and PDEs related to geometry will be introduced.

In his book, Shimura constructed the ray class field of some particular conductor over a given real quadratic field by adjoining ideal section points of Jacobian variety of a modular curve.To understand his methods, I will survey some properties of common eigen forms of Hecke operators and some theories about abelian varieties. explain some problems related to it. And then I will consider some problems related to Shimura's construction.

We define a heat kernel for Markov process and consider the problem of estimating heat kernels in both continuous and non-continuous Markov processes.