Sunday, June 12, 2022

2022-06-16 / 16:00 ~ 17:00

by ()

Over the recent years, various methods based on deep neural networks have been developed and utilized in a wide range of scientific fields. Deep neural networks are highly suitable for analyzing time series or spatial data with complicated dependence structures, making them particularly useful for environmental sciences and biosciences where such type of simulation model output and observations are prevalent. In this talk, I will introduce my recent efforts in utilizing various deep learning methods for statistical analysis of mathematical simulations and observational data in those areas, including surrogate modeling, parameter estimation, and long-term trend reconstruction. Various scientific application examples will also be discussed, including ocean diffusivity estimation, WRF-hydro calibration, AMOC reconstruction, and SIR calibration.

2022-06-15 / 16:00 ~ 17:00

IBS-KAIST 세미나 - IBS-KAIST 세미나:

by ()

In addition to diffusive signals, cells in tissue also communicate via long, thin cellular protrusions, such as airinemes in zebrafish. Before establishing communication, cellular protrusions must find their target cell. In this talk, we demonstrate that the shapes of airinemes in zebrafish are consistent with a persistent random walk model. The probability of contacting the target cell is maximized for a balance between ballistic search (straight) and diffusive search (highly curved, random). We find that the curvature of airinemes in zebrafish, extracted from live cell microscopy, is approximately the same value as the optimum in the simple persistent random walk model. We also explore the ability of the target cell to infer direction of the airineme’s source, finding that there is a theoretical trade-off between search optimality and directional information. This provides a framework to characterize the shape, and performance objectives, of non-canonical cellular protrusions in general.

2022-06-13 / 16:00 ~ 17:00

IBS-KAIST 세미나 - 수리생물학:

by ()

The connection between deep neural networks and ordinary differential equations (ODEs) is an active field of research in machine learning. In this talk, we view the hidden states of a neural network as a continuous object governed by a dynamical system. The underlying vector field is written using a dictionary representation motivated by the equation discovery method. Within this framework, we develop models for two particular machine learning tasks: time-series classification and dimension reduction. We train the parameters in the models by minimizing a loss, which is defined using the solution to the governing ODE. To attain a regular vector field, we introduce a regularization term measuring the mean total kinetic energy of the flow, which is motivated by optimal transportation theory. We solve the optimization problem using a gradient-based method where the gradients are computed via the adjoint method from optimal control theory. Through various experiments on synthetic and real-world datasets, we demonstrate the performance of the proposed models. We also interpret the learned models by visualizing the phase plots of the underlying vector field and solution trajectories.

2022-06-14 / 10:00 ~ 11:30

학과 세미나/콜로퀴엄 - 박사논문심사: 유사-Anosov 사상의 위상적 및 동역학적 성질과 호몰로지에 대한 작용

by Philippe Aurelio Tranchida(KAIST)

심사위원장 : 백형렬, 심사위원 : 박정환, 최서영, 김상현(겸직교수), 이계선(서울대학교)

2022-06-13 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Twin-width and forbidden subdivisions

by Amadeus Reinald(ENS de Lyon / IBS 이산수학그룹)

Twin-width is a recently introduced graph parameter based on vertex contraction sequences. On classes of bounded twin-width, problems expressible in FO logic can be solved in FPT time when provided with a sequence witnessing the bound. Classes of bounded twin-width are very diverse, notably including bounded rank-width, $\Omega ( \log (n) )$-subdivisions of graphs of size $n$, and proper minor closed classes. In this talk, we look at developing a structural understanding of twin-width in terms of induced subdivisions. Structural characterizations of graph parameters have mostly looked at graph minors, for instance, bounded tree-width graphs are exactly those forbidding a large wall minor. An analogue in terms of induced subgraphs could be that, for sparse graphs, large treewidth implies the existence of an induced subdivision of a large wall. However, Sintiari and Trotignon have ruled out such a characterization by showing the existence of graphs with arbitrarily large girth avoiding any induced subdivision of a theta ($K_{2,3}$). Abrishami, Chudnovsky, Hajebi and Spirkl have recently shown that such (theta, triangle)-free classes have nevertheless logarithmic treewidth. After an introduction to twin-width and its ties to vertex orderings, we show that theta-free graphs of girth at least 5 have bounded twin-width. Joint work with Édouard Bonnet, Eun Jung Kim, Stéphan Thomassé and Rémi Watrigant.

2022-06-13 / 16:30 ~ 17:30

학과 세미나/콜로퀴엄 - 대수기하학: Construction of monotone Lagrangian tori in flag varieties via toric degenerations

by 조윤형(성균관대)

A monotone symplectic manifold is a symplectic analogue of a smooth Fano variety and it provides an important classes of objects, called monotone Lagrangian tori, in view of mirror symmetry. In this talk, I will explain a way of producing monotone Lagrangian tori in a given smooth Fano variety using toric degeneration. Using this technique, we prove that there exist infinitely many monotone Lagrangian tori not Hamiltonian isotopic to each other in a full flag variety. This is based on joint work with Myungho Kim, Yoosik Kim, Jaehoon Kwon, and Euiyong Park at Center for Quantum Structures in Modules and Spaces (QSMS).

2022-06-13 / 15:15 ~ 16:15

학과 세미나/콜로퀴엄 - 대수기하학: Reconstruction problem for toric log del Pezzo surfaces using semicascades

by 황동선(IBS-CCG)

Given a space, one can study its singularities. The converse direction is called reconstruction problem: How to reconstruct spaces from given singularity information? In this talk, by introducing a notion called a semicascade we derive a bound of Picard number for toric log del Pezzo surfaces in terms of the singular points generalizing some results of Dais and Suyama, which solves the reconstruction problem with the help of computer. We also discuss Kähler-Einstein toric log del Pezzo surfaces as an application of semicascades.

2022-06-13 / 14:00 ~ 15:00

학과 세미나/콜로퀴엄 - 대수기하학: Vector bundles on surfaces and singular degeneration

by 조용화(IBS-CCG)

For the last decade, there have been a number of studies reporting that certain surface singularities give rise to vector bundle on their smoothing. The first result is by Hacking, who studies this correspondence for Wahl singularities. I am going to introduce a generalization of Hacking's result to singularities of class T, which is a natural extension of Wahl singularities. Also, if time permits, I will introduce a recent result of Tevelev-Urzua which generalizes this to arbitrary cyclic quotient surface singularities.

2022-06-13 / 14:30 ~ 16:00

학과 세미나/콜로퀴엄 - 박사논문심사: 심층신경망을 이용한 사람 치아 영상에서의 개별 치아 분할

by 김성은(KAIST)

심사위원장 : 이창옥, 심사위원 : 임미경, 김동환, 예종철(겸임교수), 김윤호(UNIST 자연과학부)

Events for the 취소된 행사 포함