Understanding complex dynamic phenomena drives scientific and technological advances in infodemiology, machine learning, or neuroscience. The body of this dissertation branches towards these three topics.

Firearm injuries are a leading cause of death in the United States, surpassing fatalities from motor vehicle crashes. Here, we elucidate the causal roles of media coverage of firearm laws and regulations, media coverage of mass shootings, media coverage of violent crimes, and the Twitter activity of anti- and pro-regulation advocacy groups in short-term firearm acquisition in the United States. We collect daily time series for these variables from 2012 to 2020 and employ the PCMCI+ framework to investigate the causal structures among them simultaneously. Our results indicate that, although media coverage of mass shootings and online activity of pro-regulation organizations are potential drivers of firearm acquisition, in the short term, the lobbying efforts of anti-regulation organizations on social media and specific media coverage appear to influence individuals’ decisions to purchase firearms directly.

Machine learning (ML) theory and industrial applications of ML differ, whereas, for the latter, data are often non-static and unlabeled. Often, trained ML models apply predictions on dissimilar data, and industrial data scientists cannot measure this dissimilarity. Naturally, questions arise about the accuracy of ML models on such dissimilar data, but the equations for measures such as accuracy require knowledge of True class labels. Answering these questions requires an adaptation of the Hui-Walter paradigm to epidemiology. Applying this approach enables practitioners to estimate key performance metrics with no prior knowledge of True class labels.

Epilepsy, a neurological disorder affecting millions worldwide, necessitates surgical intervention in the most severe cases. These interventions must target the seizure onset zone, but the lack of precise biomarkers for this zone limits surgical efficacy. Here, we use topological data analysis and Takens' embedding theorem to discover a novel biomarker not seen by the naked eye that effectively localizes the seizures in time and space from intracranial EEG.