# Study stochastic biochemical systems via their underlying network structures

강연자 김진수 포항공과대학교 2023-03-23

When a biological system is modeled using a mathematical process, the following step is normally to estimate the system parameters. Despite the numerous computational and statistical techniques, estimating parameters for complex systems can be a difficult task. As a result, one can think of revealing parameter-independent dynamical properties of a system. More precisely, rather than estimating parameters, one can focus on the underlying structure of a biochemical system to derive the qualitative behavior of the associated mathematical process. In this talk, we will discuss study of qualitative behaviors of stochastic biochemical systems using reaction networks. A reaction network is a graphical configuration of a biochemical system. One of the key problems in this field is to relate dynamical properties and the underlying reaction network structure. The goal of this talk is to 1. walk you through the basic modeling aspect of the stochastically modeled reaction networks, and 2. to show how to derive stability (ergodicity) of the associated stochastic process solely based on the underlying network structure.
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1. ### Mathemaics & Hedge Fund

헤지펀드에서 사용하고 있는 전략들을 간단히 소개하고 수학적 아이디어가 사용되는 예를 들어 퀀트의 필요한 능력을 소개한다. 수학과 헤지펀드의 관점에서 머신러닝(인공지능)의 사용 예를 설명한다.
Category수학강연회 소속지큐자산운용 강연자김택근
2. ### Satellite operators on knot concordance

Concordance is a relation which classifies knots in 3-space via surfaces in 4-space, and it is closely related with low dimensional topology. Satellite operators are one of the main tools in the study of knot concordance, and it has been wi...
Category수학강연회 소속건국대학교 강연자김태희
3. ### A dissipative effect on some PDEs with physical singularity

초록: In this lecture, we study various dissipative effect in a phase space from either entropy dissipation or boundary. We see how this effect leads mathematical studies on long time behavior and scale-uniform estimate of kinetic PDEs in g...
4. ### Study stochastic biochemical systems via their underlying network structures

When a biological system is modeled using a mathematical process, the following step is normally to estimate the system parameters. Despite the numerous computational and statistical techniques, estimating parameters for complex systems can...
Category수학강연회 소속포항공과대학교 강연자김진수
5. ### Entropy of symplectic automorphisms

※ 강연 뒷부분이 녹화되지 않았습니다. A symplectic manifold is a space with a global structure on which Hamiltonian equations are defined. A classical result by Darboux says that every symplectic manifold locally looks standard, so it has be...
Category수학강연회 소속서강대학교 강연자김준태
6. ### Circular maximal functions on the Heisenberg group

The spherical average has been a source of many problems in harmonic analysis. Since late 90's, the study of the maximal spherical means on the Heisenberg group \$mathbb{H}^n\$ has been started to show the pointwise ergodic theorems on the gro...
Category수학강연회 소속연세대 수학과 강연자김준일
7. ### The process of mathematical modelling for complex and stochastic 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 models have been widely ...
Category수학강연회 소속KAIST 강연자김재경
8. ### <학부생을 위한 ɛ 강연> 복잡한 생명현상을 위한 21세기 현미경, 수학!

지난 50년간 진행된 분자생물학의 혁명으로 인해 생명 시스템이 수많은 분자들의 상호작용으로 구성되어 있음을 알게 되었습니다. 이러한 복잡한 시스템을 이해하기 위해서는 현미경과 같이 생명현상을 관찰하는 도구와 함께 수학은 생명과학 분야에서 필수적...
Category수학강연회 소속카이스트 강연자김재경
9. ### Symplectic topology and mirror symmetry of partial flag manifolds

Soon after Gromov’s applications of pseudo-holomorphic curves to symplectic topology, Floer invented an infinite-dimensional Morse theory by analyzing moduli spaces of pseudo-holomorphic curves to make substantial progress on Arnold&r...
Category수학강연회 소속부산대학교 수학과 강연자김유식
10. ### Connectedness of a zero-level set as a geometric estimate for parabolic PDEs

Studies on PDEs are mostly focused on ?nding properties of PDEs within a speci?c discipline and on developing a technique specialized to them. However, ?nding a common structure over di?erent disciplines and unifying theories from di?erent s...
Category수학강연회 소속KAIST 강연자김용정
11. ### 곡선의 정의란 무엇인가?

곡선은 방정식, 매개화된 곡선의 동치류, 모듈 등의 다양한 관점에서 정의될 수 있다. 미끈한 곡선의 경우는 모든 정의들이 본질적으로 동등하지만 이들의 극한을 취하면 관점에 따라 완전히 다른 답들이 얻어진다. 따라서 미끈한 곡선들의 집합은 관점에 따라...
Category수학강연회 소속서울대학교 강연자김영훈
12. ### Categorification of Donaldson-Thomas invariants

In 1980s, Donaldson discovered his famous invariant of 4-manifolds which was subsequently proved to be an integral on the moduli space of semistable sheaves when the 4-manifold is an algebraic surface. In 1994, the Seiberg-Witten invariant w...
Category수학강연회 소속서울대학교 강연자김영훈
13. ### <학부생을 위한 ɛ 강연> 양자상태의 기하학

고전컴퓨터는 모든 정보를 이진수로 표현하여 계산을 0과 1의 전기신호로 구현하는데 반해서 양자컴퓨터는 정보를 벡터(양자상태)로 표현하여 유니터리 변환을 통해 계산을 수행한다. 양자컴퓨터가 관심을 끄는 이유는 얽힌 양자상태 덕분에 빠른 계산이 가능...
Category수학강연회 소속고등과학원 강연자김영훈
14. ### <정년퇴임 기념강연> 리만 가설에 관련된 옌센 다항식의 영점

Sufficient conditions for the Jensen polynomials of the derivatives of a real entire function to be hyperbolic are obtained. The conditions are given in terms of the growth rate and zero distribution of the function. As a consequence some r...
Category수학강연회 소속서울대학교 강연자김영원
15. ### On the Schauder theory for elliptic PDEs

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Category수학강연회 소속연세대학교 강연자김세익
16. ### Structural stability of meandering-hyperbolic group actions

Sullivan sketched a proof of his structural stability theorem for differentiabl group actions satisfying certain expansion-hyperbolicity axioms. We relax Sullivan’s axioms and introduce a notion of meandering hyperbolicity for group a...
Category수학강연회 소속제주대학교 강연자김성운
17. ### Iwahori-Hecke algebras and beyond

For the irreducible representations of the Hecke algebras, the minimal elements in each conjugacy class play an important role. In this talk, we try to review the minimal length elements and characterize in a more efficient way to find the m...
Category수학강연회 소속University of Picardie Jules-Verne, Amiens 강연자김성순
18. ### Introduction to Non-Positively Curved Groups

Introduction to Non-Positively Curved Groups
Category수학강연회 소속KAIST 강연자김상현