Applied Math Day
Advances in biomedical signal processing, from theory to application

DATE：2026/7/18 Sat.

LOCATION：Room 202, Astromath. Building, NTU

ORGANIZERS

• Chun-Yen Shen, Mathematics, NTU
• Mao-Pei Tsui, Mathematics, NTU
• Hau-Tieng Wu, Mathematics, NYU/AS
• Shih-Hsien Yu, Mathematics, AS

AGENDA

SPEAKERS

(1) Steven Altschuler(Systems pharmacology, UCSF)

• Title: Topics on systems biology
• Abstract: TBA

(2) Gi-Ren Liu(Mathematics, NCKU)

• Title: Probabilistic Analysis of Scalogram Ridges in Noisy Signals
• Abstract: Scalogram ridges, defined as curves tracing local maxima of the complex modulus of the wavelet transform, are widely used in time-frequency analysis of nonstationary signals. However, their statistical behavior in noisy environments is not yet well understood. In this talk, we present a probabilistic framework for studying scalogram ridges when the observed signal consists of an adaptive harmonic model corrupted by stationary Gaussian noise. We interpret ridges as a (possibly set-valued) random process obtained from the local maximizers of the scalogram along the scale direction. Within this framework, we establish several fundamental properties, including uniqueness of ridge points at fixed time and upper hemicontinuity of the ridge process. We further derive probabilistic deviation bounds that quantify how far the ridges extracted from noisy signals can deviate from those of the underlying clean signal, with explicit dependence on the signalto-noise ratio. The analysis relies on maximal inequalities for complex-valued Gaussian processes, combining tools such as the Borell-TIS inequality and Dudley’s entropy bound. Finally, we discuss the implications of our results for practical ridge extraction algorithms, including variational formulations used in applications.

(3) Satoshi Ishiwata(Mathematics, Yamagata University)

• Title: A discrete approximation of a non-symmetric diffusion on a weighted RIemannian manifold
• Abstract: In this talk, I will explain how to discretize a non-symmetric diffusion generated by the weighted Laplacian with drift and non-negative potential on a weighted Riemannian manifold by using a partition of the manifold. The contents of this talk is based on a joint work with Hiroshi Kawabi (Keio, Japan): https://link.springer.com/article/10.1007/s00208-024-02809-9

(4) Yu-Ting Lin(Anesthesiology, VGHTPE)

• Title: Compare apples and oranges by graph Laplacian
• Abstract: Biomedicine is diverse. However, we approach this field consistently by comparing the differences as the first step. Before we compare the difference between two medical images or two physiological measurements, the data acquisition comprises countless comparisons at the hardware level. The graph Laplacian is an efficient computation tool for us to handle numerous comparisons at the data analysis level. Spectral decomposition is the key mechanism. We can take advantage of it for signal processing, visualization, decomposition, and even manipulation, which will be presented with real world examples.

(5) Gal Mishne(Data Science, UCSD)

• Title: TBA 
• Abstract: TBA

(6) Ya-Ping Hsieh(Institute of Statistics, Academia Sinica)

• Title: What Do Diffusion Models Actually Learn?
• Abstract: Diffusion models are usually presented as tools for learning complex data distributions. In this talk, I will discuss a complementary view: before learning the full distribution, diffusion models first learn where the data lives. In continuous spaces, this means recovering the geometry of the data manifold before accurately modeling the density on it. In discrete spaces, such as language, it means learning validity or support structure before learning fine-grained frequencies. This perspective helps explain why diffusion models can generate realistic and novel samples even when their learned scores are still coarse. The talk will introduce the main intuition behind this “geometry-before-density” principle, explain how it appears in both continuous and discrete diffusion models, and discuss its implications for generalization, memorization, and the design of more robust generative algorithms.

(7) Tzu-Chi Liu(Mathematics, NTU)

• Title: Fast Manifold-Based Signal Recovery for Adaptive Deep Brain Stimulation
• Abstract: Adaptive deep brain stimulation relies on real-time neural biomarkers to adjust stimulation, but recorded brain signals are strongly contaminated by stimulation-induced artifacts. This work introduces SMARTA+, a computationally efficient artifact removal method designed to recover local field potentials during stimulation. The method uses a library of artifact waveforms, waveletbased features, approximate nearest-neighbor search, and adaptive template subtraction to remove time-varying stimulation artifacts. It also handles transient DC shifts that occur at stimulation onset and offset. The problem connects high-dimensional signal structure, manifold-based modeling, fast search algorithms, and real-time computation. Experiments using semi-real data and patient recordings from Parkinson’s disease patients show that SMARTA+ suppresses artifacts more effectively than conventional approaches and better preserves the timing of beta-burst events relevant to closed-loop stimulation.

(8) Gaspard Bernard(Institute of Statistics, Academia Sinica)

• Title: Time-dependent count data: estimation and forecasting in the frequency domain
• Abstract: Count data observed over time arise naturally in many applications, for example as weekly numbers of disease cases, hospital admissions, or reported events. Such observations form integer-valued time series: sequences of nonnegative integer-valued random variables that may exhibit nontrivial time dependence. In practice, these data often display two important features: a large amount of zeros, known as zero inflation, and variability much larger than predicted by a Poisson model, known as overdispersion. In some applications, this overdispersion is also associated with extreme counts and heavy-tailed processes. A classical way to model dependent count data is through integervalued autoregressive and moving-average models. In this talk, we consider such models with discretestable innovations, which provide a flexible framework for accommodating both zero inflation and potentially heavy-tailed count distributions. The goal is to estimate the model parameters consistently and use them to produce reliable forecasts. For many stationary time series, frequency-domain methods are based on the spectral density, obtained as the Fourier transform of the autocovariance function. This representation is powerful because it decomposes temporal dependence across frequencies and, in some models, contains enough information to characterize the underlying process. However, when the process is very heavy-tailed, the covariance function may fail to exist, and the classical spectral density is no longer available. To overcome this difficulty, we use a generalized spectrum: a frequency-domain object built from the characteristic function rather than from covariances. This generalized spectrum remains well defined even in settings where second moments are infinite. We show that, for the models considered, the model parameters are identifiable from this frequency-domain representation. We show that this leads to estimators that are root-n consistent and asymptotically Gaussian. Finally, we illustrate the method on weekly measles counts in Germany and show how the estimated model can be used for one-step-ahead forecasting.

Registration：[LINK]