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X-WR-CALNAME:Biomedical Mathematics Group
X-ORIGINAL-URL:https://www.ibs.re.kr/bimag
X-WR-CALDESC:Events for Biomedical Mathematics Group
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TZID:Asia/Seoul
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DTSTART:20250101T000000
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DTSTART;TZID=Asia/Seoul:20260706T100000
DTEND;TZID=Asia/Seoul:20260706T110000
DTSTAMP:20260701T084146Z
CREATED:20260616T012906Z
LAST-MODIFIED:20260701T084146Z
UID:12611-1783332000-1783335600@www.ibs.re.kr
SUMMARY:The effect of the fitness gradient - Jakub Svoboda
DESCRIPTION:Abstract: \nEvolutionary biology studies populations of reproducing individuals and how their composition changes over time.An important question is the fixation probability of a single mutant that attempts to invade a homogeneous population.Many real populations experience gradients of chemicals or nutrients that cause mutations to be beneficial in some spatial regions and harmful in others.We will examine the fixation probability of a mutant placed on a simple one-dimensional spatial structure that experiences such a gradient.The mutant’s fitness varies linearly but is on average 1\, whereas the resident’s fitness is constant and equal to 1.We will prove nonintuitive results about the fixation probability of mutants.
URL:https://www.ibs.re.kr/bimag/event/the-effect-of-the-fitness-gradient-jakub-svoboda/
LOCATION:B232 Seminar Room\, IBS\, 55 Expo-ro Yuseong-gu\, Daejeon\, Daejeon\, 34126\, Korea\, Republic of
CATEGORIES:Biomedical Mathematics Seminar
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DTSTART;TZID=Asia/Seoul:20260709T100000
DTEND;TZID=Asia/Seoul:20260709T110000
DTSTAMP:20260708T001039Z
CREATED:20260708T001039Z
LAST-MODIFIED:20260708T001039Z
UID:12695-1783591200-1783594800@www.ibs.re.kr
SUMMARY:Advanced Iterative Methods as Elementary Iterations on Larger Spaces - Jongho Park
DESCRIPTION:Abstract: \nA central goal of scientific computing is to develop accurate and efficient solvers for scientific problems\, and this goal is often pursued through sophisticated numerical methods. In modern machine learning\, by contrast\, the basic optimization procedure is often comparatively simple\, typically gradient descent and its variants\, while much of the complexity is shifted to larger models. This talk examines this contrast from the viewpoint of scientific computing.We show that many advanced iterative methods\, including domain decomposition and multigrid methods\, can be interpreted as elementary iterations applied to equivalent problems posed on larger spaces. For example\, a classical multigrid method can be viewed as a Gauss–Seidel iteration for a suitable expanded system associated with a multilevel frame. To make this interpretation rigorous\, we introduce an auxiliary-space framework that recasts an iterative method for the original system as an equivalent\, but more elementary\, method for a lifted auxiliary system.The framework applies to a broad range of advanced methods. We illustrate its utility through applications to various modern iterative methods. Finally\, we discuss how this viewpoint can inform the design of numerical methods for problems arising in machine learning.
URL:https://www.ibs.re.kr/bimag/event/advanced-iterative-methods-as-elementary-iterations-on-larger-spaces-jongho-park/
LOCATION:B232 Seminar Room\, IBS\, 55 Expo-ro Yuseong-gu\, Daejeon\, Daejeon\, 34126\, Korea\, Republic of
CATEGORIES:Biomedical Mathematics Seminar
ORGANIZER;CN="Jae Kyoung Kim":MAILTO:jaekkim@kaist.ac.kr
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DTSTART;TZID=Asia/Seoul:20260728T160000
DTEND;TZID=Asia/Seoul:20260728T170000
DTSTAMP:20260713T132333Z
CREATED:20260713T061641Z
LAST-MODIFIED:20260713T132333Z
UID:12698-1785254400-1785258000@www.ibs.re.kr
SUMMARY:Global Linearization of Nonlinear Dynamics via Koopman Operators: A Gentle Introduction\, Applications\, and Open Challenges - Hyukpyo Hong
DESCRIPTION:Abstract: \nA central challenge of modern dynamical systems theory is to make nonlinear systems tractable without sacrificing fidelity. Koopman operator theory pursues this goal by lifting nonlinear dynamics into a linear\, but infinite dimensional\, operator acting on a function space. This operator-theoretic perspective underlies a broad class of modern data-driven methods\, from dynamic mode decomposition to equation discovery in scientific machine learning for fluid dynamics and neuroscience. Yet this power comes at a price: the operator’s infinite dimensionality poses a fundamental obstacle to computation and practical use\, and finding tractable finite-dimensional approximations remains an open and active challenge. In this talk\, I will first introduce the basic principles of Koopman operator theory and survey some of the results that have made it a cornerstone of modern dynamical systems analysis. I will then briefly describe two of my works on finite-dimensional Koopman representations. Finally\, I will turn to my recent work on non-autonomous dynamical system learning\, in collaboration with Prof. Dae Wook Kim.
URL:https://www.ibs.re.kr/bimag/event/global-linearization-of-nonlinear-dynamics-via-koopman-operators-a-gentle-introduction-applications-and-open-challenges-hyukpyo-hong/
LOCATION:108\, Conference Room\, IBS\, 55 Expo-ro Yuseong-gu\, Daejeon\, Korea\, Republic of
CATEGORIES:Biomedical Mathematics Seminar
ORGANIZER;CN="Jae Kyoung Kim":MAILTO:jaekkim@kaist.ac.kr
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