Unraveling Pattern-Based Mechanics Defining Self-Organized Recurrent Behaviors in a Complex System: A Zebrafish's Calcium Brain-Wide Imaging Example - Hsieh, Fushing; Zheng, Jingyi (Frontiers in Applied Mathematics and Statistics, 2019)
Data-driven computational methodologies are developed to encode a system's spatiotemporal recording video into a global system-state trajectory, and extract a patterned signature that mechanistically defines recurrent events exhibited by a large complex system. Our developments begin by selecting informative units from various spatial regions, among which we compute mutual conditional entropy to map out an organization of communities. Each community is taken as a potential mechanism operating across several different regions. Unsupervised machine learning algorithms are employed on each community to identify a functional collection of local system-states, and then its corresponding local system-state trajectory is used as a mechanistic representation of the community. We further synthesize all local system-states trajectories to identify global dependency and global system-states. Such a spatiotemporal structural dependency points out which communities are main driving forces underlying the recurrent dynamics, and at the same time offers a patterned signature that prescribes a mechanics driving all recurrent events along the global system-state trajectory. We illustrate our data-driven computing through a brain-wide calcium imaging video of a PTZ-induced epileptic Zebrafish, and explicitly show the system-wise patterned signature as a mechanics that characteristically defines epileptic seizures.