Friday, November 4, 2022

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2022-11-08 / 17:00 ~ 18:00
학과 세미나/콜로퀴엄 - Mathematics & Beyond Seminar: 인쇄
by 김대환((주)소만사 대표이사)

2022-11-08 / 17:00 ~ 18:00
학과 세미나/콜로퀴엄 - Mathematics & Beyond Seminar: 인쇄
by 김대환((주)소만사 대표이사)

2022-11-11 / 11:00 ~ 12:00
학과 세미나/콜로퀴엄 - 응용 및 계산수학 세미나: 인쇄
by ()
Neural networks (NNs) are currently changing the computational paradigm on how to combine data with mathematical laws in physics and engineering in a profound way, tackling challenging inverse and ill-posed problems not solvable with traditional methods. However, quantifying errors and uncertainties in NN-based inference is more complicated than in traditional methods. Although there are some recent works on uncertainty quantification (UQ) in NNs, there is no systematic investigation of suitable methods towards quantifying the total uncertainty effectively and efficiently even for function approximation, and there is even less work on solving partial differential equations and learning operator mappings between infinite-dimensional function spaces using NNs. In this talk, we will present a comprehensive framework that includes uncertainty modeling, new and existing solution methods, as well as evaluation metrics and post-hoc improvement approaches. To demonstrate the applicability and reliability of our framework, we will also present an extensive comparative study in which various methods are tested on prototype problems, including problems with mixed input-output data, and stochastic problems in high dimensions.
2022-11-08 / 16:00 ~ 17:00
IBS-KAIST 세미나 - 수리생물학: 인쇄
by ()
Shift workers experience profound circadian disruption due to the nature of their work, which often has them working at times when their internal clock is sending a strong signal for sleep. Mathematical models can be used to generate recommendations for shift workers that shift their body’s clock to better align with their work schedules, to help them sleep, feel, and perform better. In this talk, I will discuss our recent mobile app, Shift, which pulls wearable data from user’s devices and generates personalized recommendations to help them manage shift work schedules. I will also discuss how this product was designed, how it can interface with Internet of Things devices, and how its insights can be useful for other groups beyond shift workers.
2022-11-09 / 16:00 ~ 17:00
IBS-KAIST 세미나 - IBS-KAIST 세미나: 인쇄
by ()
Cells make individual fate decisions through linear and nonlinear regulation of gene network, generating diverse dynamics from a single reaction pathway. In this colloquium, I will present two topics of our recent work on signaling dynamics at cellular and patient levels. The first example is about the initial value of the model, as a mechanism to generate different dynamics from a single pathway in cancer and the use of the dynamics for stratification of the patients [1-3]. Models of ErbB receptor signaling have been widely used in prediction of drug sensitivity for many types of cancers. We trained the ErbB model with the data obtained from cancer cell lines and predicted the common parameters of the model. By simulation of the ErbB model with those parameters and individual patient transcriptome data as initial values, we were able to classify the prognosis of breast cancer patients and drug sensitivity based on their in silico signaling dynamics. This result raises the question whether gene expression levels, rather than genetic mutations, might be better suited to classify the disease. Another example is about the regulation of transcription factors, the recipients of signal dynamics, for target gene expression [4-6]. By focusing on the NFkB transcription factor, we found that the opening and closing of chromatin at the DNA regions of the putative transcription factor binding sites and the cooperativity in their interaction significantly influenced the cell-to cell heterogeneity in gene expression levels. This study indicates that the noise in gene expression is rather strongly regulated by the DNA side, even though the signals are similarly regulated in a cell population. Overall these mechanisms are important in our understanding the cell as a system for encoding and decoding signals for fate decisions and its application to human diseases.
2022-11-09 / 14:00 ~ 15:00
IBS-KAIST 세미나 - IBS-KAIST 세미나: 인쇄
by ()
Wearable analytics hold far more potential than sleep tracking or step counting. In recent years, a number of applications have emerged which leverage the massive quantities of data being amassed by wearables around the world, such as real-time mood detection, advanced COVID screening, and heart rate variability analysis. Yet packaging insights from research for success in the consumer market means prioritizing design and understandability, while also seamlessly managing the sometimes-unreliable stream of data from the device. In this presentation, I will discuss my own experiences building apps which interface with wearable data and process the data using mathematical modeling, as well as recent work extending to other wearable streams and environmental controls.
2022-11-08 / 16:00 ~ 17:00
IBS-KAIST 세미나 - 수리생물학: 인쇄
by ()
Shift workers experience profound circadian disruption due to the nature of their work, which often has them working at times when their internal clock is sending a strong signal for sleep. Mathematical models can be used to generate recommendations for shift workers that shift their body’s clock to better align with their work schedules, to help them sleep, feel, and perform better. In this talk, I will discuss our recent mobile app, Shift, which pulls wearable data from user’s devices and generates personalized recommendations to help them manage shift work schedules. I will also discuss how this product was designed, how it can interface with Internet of Things devices, and how its insights can be useful for other groups beyond shift workers.
2022-11-08 / 16:30 ~ 17:30
IBS-KAIST 세미나 - 이산수학: Unified almost linear kernels for generalized covering and packing problems on nowhere dense classes 인쇄
by 안정호(KAIST & IBS 이산수학그룹)
Let $\mathcal{F}$ be a family of graphs, and let $p$ and $r$ be nonnegative integers. The $(p,r,\mathcal{F})$-Covering problem asks whether for a graph $G$ and an integer $k$, there exists a set $D$ of at most $k$ vertices in $G$ such that $G^p\setminus N_G^r[D]$ has no induced subgraph isomorphic to a graph in $\mathcal{F}$, where $G^p$ is the $p$-th power of $G$ and $N^r_G[D]$ is the set of all vertices in $G$ at distance at most $r$ from $D$ in $G$. The $(p,r,\mathcal{F})$-Packing problem asks whether for a graph $G$ and an integer $k$, $G^p$ has $k$ induced subgraphs $H_1,\ldots,H_k$ such that each $H_i$ is isomorphic to a graph in $\mathcal{F}$, and for distinct $i,j\in \{1, \ldots, k\}$, the distance between $V(H_i)$ and $V(H_j)$ in $G$ is larger than $r$. The $(p,r,\mathcal{F})$-Covering problem generalizes Distance-$r$ Dominating Set and Distance-$r$ Vertex Cover, and the $(p,r,\mathcal{F})$-Packing problem generalizes Distance-$r$ Independent Set and Distance-$r$ Matching. By taking $(p',r',\mathcal{F}')=(pt, rt, \mathcal{F})$, we may formulate the $(p,r,\mathcal{F})$-Covering and $(p, r, \mathcal{F})$-Packing problems on the $t$-th power of a graph. Moreover, $(1,0,\mathcal{F})$-Covering is the $\mathcal{F}$-Free Vertex Deletion problem, and $(1,0,\mathcal{F})$-Packing is the Induced-$\mathcal{F}$-Packing problem. We show that for every fixed nonnegative integers $p,r$ and every fixed nonempty finite family $\mathcal{F}$ of connected graphs, the $(p,r,\mathcal{F})$-Covering problem with $p\leq2r+1$ and the $(p,r,\mathcal{F})$-Packing problem with $p\leq2\lfloor r/2\rfloor+1$ admit almost linear kernels on every nowhere dense class of graphs, and admit linear kernels on every class of graphs with bounded expansion, parameterized by the solution size $k$. We obtain the same kernels for their annotated variants. As corollaries, we prove that Distance-$r$ Vertex Cover, Distance-$r$ Matching, $\mathcal{F}$-Free Vertex Deletion, and Induced-$\mathcal{F}$-Packing for any fixed finite family $\mathcal{F}$ of connected graphs admit almost linear kernels on every nowhere dense class of graphs and linear kernels on every class of graphs with bounded expansion. Our results extend the results for Distance-$r$ Dominating Set by Drange et al. (STACS 2016) and Eickmeyer et al. (ICALP 2017), and the result for Distance-$r$ Independent Set by Pilipczuk and Siebertz (EJC 2021). This is joint work with Jinha Kim and O-joung Kwon.
2022-11-11 / 16:00 ~ 17:00
학과 세미나/콜로퀴엄 - PDE 세미나: 인쇄
by 최영필(연세대)
In this talk, we discuss the Cauchy problem for the Vlasov-Riesz system, which is a Vlasov equation featuring interaction potentials generalizing various previously studied cases, including the Coulomb and Manev potentials. For the first time, we extend the local theory of classical solutions to interaction potentials which are more singular than that for the Manev. Then, we obtain finite-time singularity formation for solutions with various attractive interaction potentials, extending the well-known singularity formation result for attractive Vlasov-Poisson. Our local well-posedness and singularity formation results extend to cases with linear diffusion and damping in velocity.
2022-11-04 / 16:00 ~ 17:15
학과 세미나/콜로퀴엄 - PDE 세미나: 인쇄
by 최경수(KIAS)

2022-11-10 / 16:15 ~ 17:30
학과 세미나/콜로퀴엄 - 정수론: 인쇄
by ()
A theorem of Khare-Wintenberger and Kisin (once Serre’s modularity conjecture) says that every two-dimensional odd absolutely irreducible representation \bar\rho of the Galois group of the rationals over a finite field comes from a modular form f, that is, \bar\rho ~ \bar\rho_f. The conjecture even provides a recipe for the weight, level and character of f, but does not give any information about the slope of f. In this talk, based on joint work with Kumar, we provide conditions on f - the main one being that the weight of f is close to 0 - which guarantee that the slope of a modular form g giving rise to the twist of \bar\rho_f by the cyclotomic character has slope one more than the slope of f. This provides a global explanation of some local patterns mentioned in our first talk. The proof uses the theta operator and Coleman-Hida families of overconvergent forms. (This is the second of the two KAIX Invited Lectures.)
2022-11-08 / 16:00 ~ 17:30
학과 세미나/콜로퀴엄 - 정수론: 인쇄
by ()
The zig-zag conjecture predicts that the reductions of two-dimensional irreducible p-adic crystalline representations of half-integral slope and exceptional weights - weights which are two more than twice the slope modulo (p-1) - have reductions which are given by an alternating sequence of irreducible and reducible representations. Some partial progress was made towards this conjecture over the years by Buzzard-Gee (slope 1/2), Bhattacharya-G-Rozensztajn (slope 1) and G-Rai (slope 3/2). In this talk I shall use work of Breuil-Mézard and Guerberoff-Park in the semi-stable case and a limiting argument connecting crystalline and semi-stable representations due to Chitrao-G-Yasuda to show that zig-zag holds for half-integal slopes bounded by (p-1)/2, at least on the inertia subgroup, if the weight is sufficiently close to a weight bounded by p+1. (This is the first of the two KAIX Invited Lectures.)
2022-11-11 / 10:00 ~ 11:00
SAARC 세미나 - SAARC 세미나: 인쇄
by 윤철희(KAIST 김재철 AI 대학원)
Stochastic finite-sum optimization problems are ubiquitous in many areas such as machine learning, and stochastic optimization algorithms to solve these finite-sum problems are actively studied in the literature. However, there is a major gap between practice and theory: practical algorithms shuffle and iterate through component indices, while most theoretical analyses of these algorithms assume uniformly sampling the indices. In this talk, we talk about recent research efforts to close this theory-practice gap. We will discuss recent developments in the theoretical convergence analysis of shuffling-based optimization methods. We will first consider minimization algorithms, mainly focusing on stochastic gradient descent (SGD) with shuffling; we will then briefly talk about some new progress on minimax optimization methods.
2022-11-10 / 16:15 ~ 17:15
학과 세미나/콜로퀴엄 - 콜로퀴엄: 인쇄
by ()
In recent years, community detection has been an active research area in various fields including machine learning and statistics. While a plethora of works has been published over the past few years, most of the existing methods depend on a predetermined number of communities. Given the situation, determining the proper number of communities is directly related to the performance of these methods. Currently, there does not exist a golden rule for choosing the ideal number, and people usually rely on their background knowledge of the domain to make their choices. To address this issue, we propose a community detection method that is equipped with data-adaptive methods of finding the number of the underlying communities. Central to our method is fused l-1 penalty applied on an induced graph from the given data. The proposed method shows promising results.
Events for the 취소된 행사 포함 모두인쇄
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