NIMS 콜로퀴움

What Sparsity and $ℓ_1$ Optimization Can Do For You

• 연사: Stanley Osher (UCLA)
• 일시: 2016년 4월 8일(금) 16시
• 장소: 국가수리과학연구소 연구교류센터(CAMP) 대형세미나실
  
• Sparsity and compressive sensing have had a tremendous impact in science, technology, medicine, imaging, machine learning and now, in solving multiscale problems in applied partial differential equations, developing sparse bases for Elliptic eigenspaces and connections with viscosity solutions to Hamilton-Jacobi equations. $ℓ_1$ and related optimization solvers are a key tool in this area. The special nature of this functional allows for very fast solvers: $ℓ_1$ actually forgives and forgets errors in Bregman iterative methods.
  I will describe simple, fast algorithms and new applications ranging from image processing, machine learning to sparse dynamics for PDE.

NIMS 콜로퀴움

An Introduction to Industrial Mathematics

• 연사: T. G. Myers(Universitat Polit`ecnica de Catalunya, Barcelona, Spain)
• 일시: 2015년 11월 12일(목) 16시 30분
• 장소: 국가수리과학연구소 수학원리응용센터 대강당
  

▩ Industrial mathematics is a term used to describe a broad range of applied mathematics topics, with the common factor that the work is motivated by some problem of practical interest. In this talk I will give a brief introduction to industrial mathematics and then illustrate it with three more detailed examples.

▩ Football motion through the air. This project came from a question posed by a South African premiership team. Simply put the question was, can we choose a football that will disadvantage a visiting team. The answer was yes and the teams results improved significantly after this work was completed.

▩ Phase change. The mathematical deion of the change of phase of a substance, for example from liquid to solid, is well established. However, in certain situations the standard formulations break down. I will describe our recent work on the melting of nanoparticles and solidification of a supercooled liquid.

▩ Flow in carbon nanotubes. Carbon nanotubes are viewed as one of the most exciting new materials with applications in electronics, optics, materials science and architecture. One unusual property is that liquid flows through nanotubes have been observed up to five orders of magnitude faster than predicted by classical fluid dynamics. I will describe a model for fluid flow in a CNT and show that the theoretical limit is closer to 50 times the classical value. This result is in keeping with later experimental and molecular dynamics papers.

NIMS 콜로퀴움

□ 연사: 김재경 교수 (KAIST)
□ 일시: 2015년 9월 22일(화) 16시30분
□ 장소: 국가수리과학연구소 수학원리응용센터 대강당
□ 제목 : Introduction for the application of mathematics to understand complex biological systems

 The revolution of molecular biology in the early 1980s has revealed complex network of non-linear and stochastic biochemical interactions underlying biological systems. To understand this complex system, mathematical modeling has been widely used.
 In this talk, I will introduce the typical process of applying mathematical models to biological systems including mathematical representation of biological systems, model fitting to data, analysis and simulations, and experimental validation. I will also describe our efforts to develop and integrate mathematical tools across the different steps of the modeling process. 

 Finally, I will discuss the shortcomings of our present approach and how they point to the parts of current toolbox of mathematical biology that need further mathematical development.

NIMS Colloquium

■ 연 사 : Bernd Sturmfels 교수 (UC Berkeley) 

■ 일 시 : 2015년 7월 23일(목) 16시30분

■ 장 소 : 국가수리과학연구소 수학원리응용센터(CAMP) 대강당

■ Title: Rational Design of Antibiotic Treatment Plans

■ Abstract : We present work with Portia Mira, Kristina Crona, Devin Greene, Juan Meza and Miriam Barlow, aimed at developing antibiotic treatment plans that can reverse the evolution of antibiotic resistance. The Barlow lab at UC Merced generated adaptive landscapes for 16 genotypes of the TEM beta-lactamase that vary from the wild type genotype TEM-1 through all combinations of four amino acid substitutions, and determined the growth rate of each genotype when treated with each of 15 beta-lactam antibiotics. Using growth rates for fitness in two models from population genetics, we computed the probability of each amino acid substitution in each beta-lactam treatment, and we searched through the 15 treatments for substitution paths leading from each of the 16 genotypes back to TEM-1. We identified treatment paths with the highest probabilities of returning TEM to the wild type state, thus offering promise for reversing the evolution of resistance to antibiotics. This lecture highlights the mathematics in this project.

NIMS 콜로퀴움

연사: Jiang Zeng(Universit&eae; Claude Bernard Lyon-I)

일시: 2015년 6월 18일(목)

장소: 국가수리과학연구소 CAMP 중형세미나실

Title: Combinatorics around two extensions of Hermite polynomials

Abstract
We will highlight two examples of the interplay of combinatorics and
orthogonal polynomials by considering two recent one-parameter extensions of Hermite polynomials:
a curious q-analog in connection with q-Weyl algebra and the 2D-Hermite polynomials.
As application we derive a generalization of Touchard-Riordan formula for
crossings of chords joining pairs of 2n points on a circle and a new Kibble-Slepian type
formula for the 2D-Hermite polynomials, which extends the Poisson kernel for these polynomials.

NIMS  Colloquium

Spectral theory of Neumann-Poincare Operator and applications

연사 : 강현배 교수(인하대학교)
일시 : 2015년 5월 22일(금) 16:30
장소 : 국가수리과학연구소 3층 세미나실

Abstract

The Neumann-Poincare (NP) operator is a boundary integral operator which arises naturally when solving boundary value problems using layer potentials. It is not self-adjoint with the usual inner product. But it can symmetrized by introducing a new inner product on H−1/2 spaces using Plemelj's symmetrizationprinciple. Recently many nteresting spectral properties of the NP operator have been discovered. I will discuss about this development and various applications including solvability of PDEs with complex coefficients and plasmonicresonance.