Friday, May 17, 2024

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

학과 세미나/콜로퀴엄 - 박사논문심사:

by ()

2024-05-22 / 13:30 ~ 14:30

학과 세미나/콜로퀴엄 - 위상수학 세미나:

by ()

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 1: What are PCF rational maps?] We begin by introducing PCF rational maps, highlighting their significance in complex dynamics.

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

학과 세미나/콜로퀴엄 - 기타:

by ()

(Dynamics Seminar)

2024-05-22 / 10:30 ~ 11:30

학과 세미나/콜로퀴엄 - 위상수학 세미나:

by ()

(John Hubbard's Mini-course: Lecture 1)

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.

2024-05-21 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Graph problems and monotone classes

by Vadim Lozin(University of Warwick)

Very little is known about critical properties of graphs in the hierarchy of monotone classes, i.e. classes closed under taking (not necessarily induced) subgraphs. We distinguish four important levels in this hierarchy and discuss possible new levels by focusing on the Hamiltonian cycle problem. In particular, we obtain a number of results for this problem on monotone classes.

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.

2024-05-17 / 14:00 ~ 16:00

IBS-KAIST 세미나 - IBS-KAIST 세미나:

by 황규영(IBS 의생명수학그룹)

"Optimal-Transport Analysis of Single-Cell Gene Expression Identifies Developmental Trajectories in Reprogramming", Cell (2019) will be discussed in this Journal Club. Understanding the molecular programs that guide differentiation during development is a major challenge. Here, we introduce Waddington-OT, an approach for studying developmental time courses to infer ancestor-descendant fates and model the regulatory programs that underlie them. We apply the method to reconstruct the landscape of reprogramming from 315,000 single-cell RNA sequencing (scRNA-seq) profiles, collected at half-day intervals across 18 days. The results reveal a wider range of developmental programs than previously characterized. Cells gradually adopt either a terminal stromal state or a mesenchymal-to-epithelial transition state. The latter gives rise to populations related to pluripotent, extra-embryonic, and neural cells, with each harboring multiple finer subpopulations. The analysis predicts transcription factors and paracrine signals that affect fates and experiments validate that the TF Obox6 and the cytokine GDF9 enhance reprogramming efficiency. Our approach sheds light on the process and outcome of reprogramming and provides a framework applicable to diverse temporal processes in biology. If you want to participate in the seminar, you need to enter IBS builiding (https://www.ibs.re.kr/bimag/visiting/). Please contact if you first come IBS to get permission to enter IBS building.

2024-05-17 / 14:00 ~ 16:00

학과 세미나/콜로퀴엄 - 기타: Introduction to étale cohomology 5

by 이제학(KAIST)

This is an introductory reading seminar presented by a senior undergraduate student, Jaehak Lee, who is studying the subject.

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.

2024-05-21 / 16:00 ~ 17:00

SAARC 세미나 - SAARC 세미나:

by 김바라(고려대학교)

This presentation focuses on unbiased simulation methods for quantities associated with sample paths from stochastic differential equations. Unbiased simulation methods can be found by changing probability measures with appropriately selecting the Radon-Nikodym derivative processes. I propose an unbiased Monte-Carlo simulation method that can be used even when the Girsanov kernel for the change of probability measures is not bounded. Then, I illustrate its practical application through an example involving unbiased Monte Carlo simulation for pricing the continuously averaging arithmetic Asian options under the Black-Scholes model.

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

학과 세미나/콜로퀴엄 - 콜로퀴엄:

by ()

Events for the 취소된 행사 포함