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2016 NCTS/CMMSC Seminars on Probability and Statistics

Date 2016-01-07
Time 10:00-12:20
Venue SA223
Abstract Time:10:00~12:20, January 7th, 2016(Thursday)
Place: Room 223, Science Building I, NCTU

Topic I: Concentration of Frequency and Time
Speaker:吳浩榳 教授 (加拿大多倫多大學數學系)

Topic II:Vector Diffusion maps and its application to image de-noising
Speaker:林楨芸 博士 (加拿大多倫多大學數學系)

Topic III: Phenomenological Modeling and Quantification of the Three Physiological Phenomena in Electrocardiography during General Anesthesia
Speaker:林祐霆 博士 (新光吳火獅紀念醫院麻醉科醫師)

講題: Concentration of Frequency and Time
主講人:吳浩榳 教授 (加拿大多倫多大學數學系)
Concentration of frequency and time (ConceFT) is a recently developed time-frequency representation tool. It helps to extract dynamical information hidden inside a given time series, and generalizes our understanding of power spectrum or spectrogram. It depends on the nonlinear time-frequency analysis, like synchrosqueezing transform, the multi-taper analysis and high dimensional geometric properties of noise. The extracted dynamical features could be the input to other high dimensional data analysis tools.

講題: Vector Diffusion maps and its application to image de-noising
主講人:林楨芸 博士 (加拿大多倫多大學數學系)
Dimension reduction is useful in high dimensional time series analysis. As data sets often have certain nonlinear structures, nonlinear dimensionality reduction techniques are getting increasingly popular. One such a method is vector diffusion maps (VDM) which are defined by eigen-vector fields of the connection Laplacian. In this talk, I will discuss local embedding of manifolds via eigen-vector fields of the connection Laplacian which explains why VDM gives good representations of the data in a low dimensional Euclidean space. For data sets, the eigen-vector fields can be computed by the graph connection Laplacian (GCL). I will also discuss the mathematical framework of the image de-noising method, vector nonlocal mean filter, using the GCL.

講題: Phenomenological Modeling and Quantification of the Three Physiological Phenomena in Electrocardiography during General Anesthesia
主講人:林祐霆 醫師 (新光吳火獅紀念醫院麻醉科)
General anesthesia is a unique condition for human body. Facing the sleeping patient, we often rely on patient monitor to support our administration of anesthesia. From the instantaneous heart rate (IHR) information deriving from electrocardiography (ECG), I discovered three physiological phenomena that are seldom or never been reported. They are 1) “rhythmic to non-rhythmic phenomenon”, 2) “low frequency (LF) surge phenomenon” 3) “multiple component phenomenon”. All are related with the anesthesia and surgery in a dynamic manner. Moreover, all these kinds of information are nearly impossible to be read from the currently standard patient monitor using our naked eye. The pursuit of my research problems regarding these phenomena led to a phenomenological model, which contains their behaviors, helps my understanding, and supports the data analysis to gain the potential clinical values.
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