Thursday, May 23, 2024

2024-05-27 / 16:30 ~ 17:30

학과 세미나/콜로퀴엄 - 박사논문심사:

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2024-05-23 / 12:00 ~ 13:00

학과 세미나/콜로퀴엄 - 박사논문심사:

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2024-05-28 / 10:00 ~ 11:00

학과 세미나/콜로퀴엄 - 박사논문심사:

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2024-05-30 / 10:00 ~ 11:00

학과 세미나/콜로퀴엄 - 박사논문심사:

by 채석주()

2024-05-29 / 13:30 ~ 14:30

학과 세미나/콜로퀴엄 - 위상수학 세미나:

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Post-critically finite (PCF) rational maps are a fascinating class of dynamical systems with rich mathematical structures. In this minicourse, we explore the interplay between topology, geometry, and dynamics in the study of PCF rational maps. [Lecture 3: Geometry of PCF rational maps] Geometry of PCF rational maps The topological models for PCF rational maps we discuss define canonical quasi-symmetric classes of metrics on their Julia sets. We investigate the conformal dimensions of Julia sets, which measure their geometric complexity and provide insights into the underlying dynamics. Through this exploration, we uncover the intricate relationship between the topology, geometry, and dynamics of PCF rational maps.

2024-05-27 / 13:30 ~ 14:30

학과 세미나/콜로퀴엄 - 위상수학 세미나:

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Post-critically finite (PCF) rational maps are a fascinating class of dynamical systems with rich mathematical structures. In this minicourse, we explore the interplay between topology, geometry, and dynamics in the study of PCF rational maps. [Lecture 2: Topology of PCF rational maps] W.Thurston's and D.Thurston's characterizations provide powerful frameworks for understanding the topological dynamics of rational maps. We delve into these characterizations, exploring their implications for the dynamics of PCF rational maps. Additionally, we discuss finite subdivision rules and topological surgeries, such as matings, tunings, and decompositions, as tools for constructing and analyzing PCF rational maps in topological ways.

2024-05-29 / 10:30 ~ 11:30

학과 세미나/콜로퀴엄 - 위상수학 세미나:

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(John Hubbard's Mini-course: Lecture 3)

2024-05-27 / 10:30 ~ 11:30

학과 세미나/콜로퀴엄 - 위상수학 세미나:

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(John Hubbard's Mini-course: Lecture 2)

2024-05-23 / 09:30 ~ 11:00

학과 세미나/콜로퀴엄 - 기타:

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(Dynamics Seminar)

2024-05-24 / 11:00 ~ 12:00

학과 세미나/콜로퀴엄 - 응용 및 계산수학 세미나:

by 박경덕(연세대학교)

Quantum embedding is a fundamental prerequisite for applying quantum machine learning techniques to classical data, and has substantial impacts on performance outcomes. In this study, we present Neural Quantum Embedding (NQE), a method that efficiently optimizes quantum embedding beyond the limitations of positive and trace-preserving maps by leveraging classical deep learning techniques. NQE enhances the lower bound of the empirical risk, leading to substantial improvements in classification performance. Moreover, NQE improves robustness against noise. To validate the effectiveness of NQE, we conduct experiments on IBM quantum devices for image data classification, resulting in a remarkable accuracy enhancement. In addition, numerical analyses highlight that NQE simultaneously improves the trainability and generalization performance of quantum neural networks, as well as of the quantum kernel method.

2024-05-23 / 13:00 ~ 14:00

학과 세미나/콜로퀴엄 - 응용수학 세미나:

by 권정열()

Reinforcement learning (RL) has become one of the most central problems in machine learning, showcasing remarkable success in recommendation systems, robotics and super-human level game plays. Yet, existing literature predominantly focuses on (almost) fully observable environments, overlooking the complexities of real-world scenarios where crucial information remains hidden. In this talk, we consider reinforcement learning in partially observable systems through the proposed framework of the Latent Markov Decision Process (LMDP). In LMDPs, an MDP is randomly drawn from a set of possible MDPs at the beginning of the interaction, but the context -- the latent factors identifying the chosen MDP -- is not revealed to the agent. This opacity poses new challenges for decision-making, particularly in scenarios like recommendation systems without sensitive user data, or medical treatments for undiagnosed illnesses. Despite the significant relevance of LMDPs to real-world problems, existing theories rely on restrictive separation assumptions -- an unrealistic constraint in practical applications. We present a series of new results addressing this gap: from leveraging higher-order information to develop sample-efficient RL algorithms, to establishing lower bounds and improved results under more realistic assumptions within Latent MDPs.

2024-05-24 / 13:30 ~ 14:30

학과 세미나/콜로퀴엄 - 기타:

by 임선혁(성균관대)

We provide general upper and lower bounds for the Gromov–Hausdorff distance d_GH(S^m, S^n) between spheres S^m and S^n (endowed with the round metric) for 0 <= m < n <= 1. Some of these lower bounds are based on certain topological ideas related to the Borsuk–Ulam theorem. Via explicit constructions of (optimal) correspondences, we prove that our lower bounds are tight in the cases of d_GH(S^0, S^n), d_GH(S^m, S^\infty), d_GH(S^1, S^2), d_GH(S^1, S^3), and d_GH(S^2, S^3). We also formulate a number of open questions.

2024-05-24 / 14:00 ~ 16:00

IBS-KAIST 세미나 - IBS-KAIST 세미나:

by (IBS 의생명수학그룹)

"PenDA, a rank-based method for personalized differential analysis: Application to lung cancer", Plos Comp. Biol. (2020) will be discussed in this Journal Club. The hopes of precision medicine rely on our capacity to measure various high-throughput genomic information of a patient and to integrate them for personalized diagnosis and adapted treatment. Reaching these ambitious objectives will require the development of efficient tools for the detection of molecular defects at the individual level. Here, we propose a novel method, PenDA, to perform Personalized Differential Analysis at the scale of a single sample. PenDA is based on the local ordering of gene expressions within individual cases and infers the deregulation status of genes in a sample of interest compared to a reference dataset. Based on realistic simulations of RNA-seq data of tumors, we showed that PenDA outcompetes existing approaches with very high specificity and sensitivity and is robust to normalization effects. Applying the method to lung cancer cohorts, we observed that deregulated genes in tumors exhibit a cancer-type-specific commitment towards up- or down-regulation. Based on the individual information of deregulation given by PenDA, we were able to define two new molecular histologies for lung adenocarcinoma cancers strongly correlated to survival. In particular, we identified 37 biomarkers whose up-regulation lead to bad prognosis and that we validated on two independent cohorts. PenDA provides a robust, generic tool to extract personalized deregulation patterns that can then be used for the discovery of therapeutic targets and for personalized diagnosis. An open-access, user-friendly R package is available at https://github.com/bcm-uga/penda. If you want to participate in the seminar, you need to enter IBS builiding (https://www.ibs.re.kr/bimag/visiting/). Please contact jaekkim@kaist.ac.kr if you first come IBS to get permission to enter IBS building.

2024-05-28 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Three-way online correlated selection

by 신용호(연세대)

Two-way online correlated selection (two-way OCS) is an online algorithm that, at each timestep, takes a pair of elements from the ground set and irrevocably chooses one of the two elements, while ensuring negative correlation in the algorithm's choices. OCS was initially invented by Fahrbach, Huang, Tao, and Zadimoghaddam (FOCS 2020, JACM 2022) to break a natural long-standing barrier in edge-weighted online bipartite matching. They posed two open questions, one of which was the following: Can we obtain n-way OCS for $n >2$, in which the algorithm can be given $n >2$ elements to choose from at each timestep? In this talk, we affirmatively answer this open question by presenting a three-way OCS which is simple to describe: it internally runs two instances of two-way OCS, one of which is fed with the output of the other. Contrast to its simple construction, we face a new challenge in analysis that the final output probability distribution of our three-way OCS is highly elusive since it requires the actual output distribution of two-way OCS. We show how we tackle this challenge by approximating the output distribution of two-way OCS by a flatter distribution serving as a safe surrogate. This is joint work with Hyung-Chan An.

2024-05-24 / 14:00 ~ 16:00

학과 세미나/콜로퀴엄 - 기타: Introduction to complex algebraic geometry and Hodge theory #6

by 김재홍(KAIST)

This is part of an informal seminar series to be given by Mr. Jaehong Kim, who has been studying the book "Hodge theory and Complex Algebraic Geometry Vol 1 by Claire Voisin" for a few months. There will be 6-8 seminars during Spring 2024, and it will summarize about 70-80% of the book.

2024-05-28 / 16:30 ~ 17:30

학과 세미나/콜로퀴엄 - 정수론:

by 이태영()

The finite quotient groups of étale fundamental groups of algebraic curves in positive characteristic are precisely determined, but without explicit construction of quotient maps, by well-known results of Raynaud, Harbater and Pop, previously known as Abhyankar's conjecture. Katz, Rojas León and Tiep have been studying the constructive side of this problem using certain "easy to remember" local systems. In this talk, I will discuss the main results and methods of this project in the case of a specific type of local systems called hypergeometric sheaves.

2024-05-28 / 16:00 ~ 17:00

SAARC 세미나 - SAARC 세미나:

by 강경근(연세대학교)

Weak discuss existence of singular solutions for Stokes and the Navier-Stokes equations in the half-space. We construct their solutions whose normal derivatives are unbounded for the Stokes and Navier-Stokes equations near boundary away from support of singular data.

2024-05-23 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄:

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