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X-WR-CALDESC:Events for Biomedical Mathematics Group
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DTSTART:20240101T000000
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DTSTART;TZID=Asia/Seoul:20250530T110000
DTEND;TZID=Asia/Seoul:20250530T120000
DTSTAMP:20260521T205422
CREATED:20250217T081212Z
LAST-MODIFIED:20250217T082031Z
UID:10780-1748602800-1748606400@www.ibs.re.kr
SUMMARY:Koopman operator approach to complex rhythmic systems - Hiroya Nakao
DESCRIPTION:Abstract \nSpontaneous rhythmic oscillations are widely observed in real-world systems. Synchronized rhythmic oscillations often provide important functions for biological or engineered systems. One of the useful theoretical methods for analyzing rhythmic oscillations is the phase reduction theory for weakly perturbed limit-cycle oscillators\, which systematically gives a low-dimensional description of the oscillatory dynamics using only the asymptotic phase of the oscillator. Recent advances in Koopman operator theory provide a new viewpoint on phase reduction\, yielding an operator-theoretic definition of the classical notion of the asymptotic phase and\, moreover\, of the amplitudes\, which characterize distances from the limit cycle. This led to the generalization of classical phase reduction to phase-amplitude reduction\, which can characterize amplitude deviations of the oscillator from the unperturbed limit cycle in addition to the phase along the cycle in a systematic manner. In the talk\, these theories are briefly reviewed and then applied to several examples of synchronizing rhythmic systems\, including biological oscillators\, networked dynamical systems\, and rhythmic spatiotemporal patterns.
URL:https://www.ibs.re.kr/bimag/event/koopman-operator-approach-to-complex-rhythmic-systems-hiroya-nakao/
LOCATION:ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium)\, (pw: 1234)
CATEGORIES:Biomedical Mathematics Online Colloquium
ATTACH;FMTTYPE=image/jpeg:https://www.ibs.re.kr/bimag/cms/wp-content/uploads/2025/02/nakao-hiroya.jpg
ORGANIZER;CN="Jae Kyoung Kim":MAILTO:jaekkim@kaist.ac.kr
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20250530T140000
DTEND;TZID=Asia/Seoul:20250530T160000
DTSTAMP:20260521T205422
CREATED:20250426T143239Z
LAST-MODIFIED:20250528T035910Z
UID:11061-1748613600-1748620800@www.ibs.re.kr
SUMMARY:Direct Estimation of Parameters in ODE Models Using WENDy - Kangmin Lee
DESCRIPTION:In this talk\, we discuss the paper “Direct Estimation of Parameters in ODE Models Using WENDy: Weak-Form Estimation of Nonlinear Dynamics” by David M. Bortz\, Daniel A. Messenger\, and Vanja Dukic\, Bulletin of Mathematical Biology\, 2023. \nAbstract \nWe introduce the Weak-form Estimation of Nonlinear Dynamics (WENDy) method for estimating model parameters for non-linear systems of ODEs. Without relying on any numerical differential equation solvers\, WENDy computes accurate estimates and is robust to large (biologically relevant) levels of measurement noise. For low dimensional systems with modest amounts of data\, WENDy is competitive with conventional forward solver-based nonlinear least squares methods in terms of speed and accuracy. For both higher dimensional systems and stiff systems\, WENDy is typically both faster (often by orders of magnitude) and more accurate than forward solver-based approaches. The core mathematical idea involves an efficient conversion of the strong form representation of a model to its weak form\, and then solving a regression problem to perform parameter inference. The core statistical idea rests on the Errors-In-Variables framework\, which necessitates the use of the iteratively reweighted least squares algorithm. Further improvements are obtained by using orthonormal test functions\, created from a set of C∞ bump functions of varying support sizes.We demonstrate the high robustness and computational efficiency by applying WENDy to estimate parameters in some common models from population biology\, neuroscience\, and biochemistry\, including logistic growth\, Lotka-Volterra\, FitzHugh-Nagumo\, Hindmarsh-Rose\, and a Protein Transduction Benchmark model. Software and code for reproducing the examples is available at https://github.com/MathBioCU/WENDy.
URL:https://www.ibs.re.kr/bimag/event/quantifying-and-correcting-bias-in-transcriptional-parameter-inference-from-single-cell-data-kangmin-lee/
LOCATION:B232 Seminar Room\, IBS\, 55 Expo-ro Yuseong-gu\, Daejeon\, Daejeon\, 34126\, Korea\, Republic of
CATEGORIES:Journal Club
ORGANIZER;CN="Jae Kyoung Kim":MAILTO:jaekkim@kaist.ac.kr
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