Biomedical Mathematics Seminar

We introduce a sufficient graphical model by applying the recently developed nonlinear sufficient dimension reduction techniques to the evaluation of conditional independence. The graphical model is nonparametric in nature, as it does not make distributional assumptions such as the Gaussian or copula Gaussian assumptions. However, unlike a fully nonparametric graphical model, which relies on the …

Abstract: TBA

We propose a kernel-based estimator to predict the mean response trajectory for sparse and irregularly measured longitudinal data. The kernel estimator is constructed by imposing weights based on the subject-wise similarity on L2 metric space between predictor trajectories, where we assume that an analogous fashion in predictor trajectories over time would result in a similar …

TBA

To understand nonparametric regression, we should know first what the parametric model is. Simply speaking, the parametric regression model consists of many assumptions and the nonparametric regression model eases the assumptions. I will introduce what assumptions the parametric regression model has and how the nonparametric regression model relieves them. In addition, their pros and cons will …

Abstract Mathematical models of biological systems, including neurons, often feature components that evolve on very different timescales. Mathematical analysis of these multi-timescale systems can be greatly simplified by partitioning them into subsystems that evolve on different time scales. The subsystems are then analyzed semi-independently, using a technique called fast-slow analysis. I will briefly describe the …

Abstract: Cell-to-cell variability in gene expression exists even in a homogeneous population of cells. Dissecting such cellular heterogeneity within a biological system is a prerequisite for understanding how a biological system is developed, homeostatically regulated, and responds to external perturbations. Single-cell RNA sequencing (scRNA-seq) allows the quantitative and unbiased characterization of cellular heterogeneity by providing …

Abstract: Through the past decades, electrophysiological experiments have revealed that extracellular electrical potential of brain show diverse rhythmic activity. Called ‘Local Field Potential(LFP)’, those rhythmic activities are thought to reflect populational activity of neurons. In this talk, I will introduce basic concepts on LFP and its generation mechanisms. Then, roles of LFP in brain inter-areal …