Subventions et des contributions :

Subvention ou bourse octroyée s'appliquant à plus d'un exercice financier. (2017-2018 à 2022-2023)

Due to the explosive progress of technology, scientists are challenged by more diverse and complicated data. Among the challenges encountered in the new data era, the main target of this 5-year research proposal is to systematically establish an analysis scheme to integrate information from heterogeneous datasets collected from multimodal instruments. The established tool allows us to extract the nonlinear and non-stationary structure hidden inside the system under observation. This is generally known as the sensor fusion problem, and this problem shows up in almost all scientific fields. One particular data type this research proposal focuses on is the multivariate time series collected from different sensors. The coupling problem among different time series could be understood as a special sensor fusion problem. In addition to establishing the mathematical and statistical theory beyond the methodology, the algorithm will be directly applied to study different medical problems.

The proposed 5-year research plan includes the following five main components. (1) The PI will generalize the manifold learning algorithm, the alternating diffusion (AD), to integrate nonlinear and non-stationary information shared by multiple sensors, and design an algorithm to extract information shared among the sensors. (2) Based on the multi-resolution idea, the principle bundle structure will be taken into account to model the dataset, which allows us a theoretical framework to analyze the AD algorithm for multiple sensors. (3) The statistical properties of the AD and the nonlinear TF analysis will be established, and the hypothesis testing will be designed for the clinical usage. (4) The PI will improve the current coupling index by taking the nonlinear time-frequency (TF) analysis and AD into account. Particularly, the novel de-shape short time Fourier transform will be combined with the stroboscopic approach to eliminate the common problems encountered in the coupling index analysis. The generalized AD algorithm, when combined with the nonlinear TF analysis, will lead to a novel adaptive coupling index (ACI). (5) To confirm the usefulness of the proposed algorithm, mathematical frameworks and the analysis, the PI will apply the ACI to study the sleep dynamics problem, the perinatal cerebral ischemia and fetal chronic hypoxia.

The established data analysis framework could be applied to different fields beyond the clinical applications we plan to focus on. It has a potential to be applied to all problems involving multiple sensors or multivariate time series, particularly when the nonlinear and non-stationary structure is the main interest of the analysis. In addition to its practical usefulness, the developed mathematical and statistical analyses results and the medical applications will together pave the road to connect mathematics and medicine.