Tuesday, May 2, 2023

2023-05-08 / 10:00 ~ 11:00

by ()

We present a framework of predictive modeling of unknown system from measurement data. The method is designed to discover/approximate the unknown evolution operator, i.e., flow map, behind the data. Deep neural network (DNN) is employed to construct such an approximation. Once an accurate DNN model for the evolution operator is constructed, it serves as a predictive model for the unknown system and enables us to conduct system analysis. We demonstrate that flow map learning (FML) approach is applicable for modeling a wide class of problems, including dynamical systems, systems with missing variables and hidden parameters, as well as partial differential equations (PDEs).

2023-05-09 / 15:00 ~ 16:30

SAARC 세미나 - SAARC 세미나:

by ()

We obtain uniform in time L^\infty -bounds for the solutions to a class of thermo-diffusive systems. The nonlinearity is assumed to be at most sub-exponentially growing at infinity and have a linear behavior near zero. This is a joint work with Lenya Ryzhik and Jean-Michel Roquejoffre.

2023-05-03 / 12:00 ~ 13:00

학과 세미나/콜로퀴엄 - 기타:

by ()

Compressible Euler system (CE) is a well-known PDE model that was formulated in the 19th century for dynamics of compressible fluid. The most important feature of CE is the finite-time breakdown of smooth solutions, especially, the formation of shock wave as severe singularity. Therefore, a fundamental question (since Riemann 1858) is on what happens after a shock occurs. This is the problem on well-posedness (that is, existence, uniqueness, stability) of CE in a suitable class of solutions. We will discuss on the well-posedness problem, and its generalization for applications to other PDE models arising in various contexts such as magnetohydrodynamics, tumor angiogenesis, vehicular traffic flow, etc.

2023-05-09 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Separating the edges of a graph by a linear number of paths

by Jozef Skokan(London School of Economics)

Recently, Letzter proved that any graph of order n contains a collection P of $O(n \log^*n)$ paths with the following property: for all distinct edges e and f there exists a path in P which contains e but not f. We improve this upper bound to 19n, thus answering a question of Katona and confirming a conjecture independently posed by Balogh, Csaba, Martin, and Pluhar and by Falgas-Ravry, Kittipassorn, Korandi, Letzter, and Narayanan. Our proof is elementary and self-contained.

2023-05-08 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - 박사논문심사: Parallel computation techniques to accelerate training of deep neural networks

by 이영규 (KAIST)()

2023-05-04 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄:

by ()

Collective cell movement is critical to the emergent properties of many multicellular systems including microbial self-organization in biofilms, wound healing, and cancer metastasis. However, even the best-studied systems lack a complete picture of how diverse physical and chemical cues act upon individual cells to ensure coordinated multicellular behavior. Myxococcus xanthus is a model bacteria famous for its coordinated multicellular behavior resulting in dynamic patterns formation. For example, when starving millions of cells coordinate their movement to organize into fruiting bodies – aggregates containing tens of thousands of bacteria. Relating these complex self-organization patterns to the behavior of individual cells is a complex-reverse engineering problem that cannot be solved solely by experimental research. In collaboration with experimental colleagues, we use a combination of quantitative microscopy, image processing, agent-based modeling, and kinetic theory PDEs to uncover the mechanisms of emergent collective behaviors.

2023-05-02 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: An exponential improvement for diagonal Ramsey

by Rob Morris(IMPA)

The Ramsey number $R(k)$ is the minimum n such that every red-blue colouring of the edges of the complete graph on n vertices contains a monochromatic copy of $K_k$. It has been known since the work of Erdős and Szekeres in 1935, and Erdős in 1947, that $2^{k/2} < R(k) < 4^k$, but in the decades since the only improvements have been by lower order terms. In this talk I will sketch the proof of a very recent result, which improves the upper bound of Erdős and Szekeres by a (small) exponential factor. Based on joint work with Marcelo Campos, Simon Griffiths and Julian Sahasrabudhe.

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