The human brain has been modeled as a complex network with a non-random multi-scale structure, and subsystems coupled by a nonlinear dynamic, capable of generating complex responses to simultaneous and diverse external inputs, and with self-organization capabilities. Understanding the connectivity of the hundreds of billions of neurons in the human brain is essential to knowing the nature of specific brain functions and physical structure. In modern network neuroscience, there are three important interrelated concepts of connectivity: structural or anatomic, functional, and effective. Functional connectivity (FC) is defined as the statistical temporal dependencies between neuronal activation events occurring in spatially separated brain regions. Resting-state functional magnetic resonance imaging (rs-fMRI) is a non-invasive imaging technique based on the blood oxygen level of the brain, widely used in network neuroscience to understand the functional connectivity of the human brain. The statistical and machine learning analyses of human brain functional networks presented in this dissertation were developed in a multi-site rs-fMRI database framework. In this dissertation, we present two groups of contributions applied to the study of the functional connectivity of the human brain network. Our first group of contributions is the design and development of GPU-based high-performance algorithms to compute: 1) The Sparse Fast Fourier Transform (SFFT) of k-sparse signals; 2) The breadth-first search algorithm; and 3) The betweenness centrality graph metric, all of which can be used for the analysis of large structural and functional brain networks. Our second group of contributions, applicable to the statistical and machine learning analysis of human brain functional networks in a multi-site resting-state functional MRI database framework, are: 1) A comprehensive approach for the solution of the problem of confounding effects over the machine learning classification models of rs-fMRI multi-site data; and 2) Assessment of time-varying functional connectivity in a multi-site data rs-fMRI data framework.

Oswaldo Artiles is a Ph.D. candidate at the Knight Foundation School of Computing & Information Sciences (KFSCIS) at Florida International University. His research focuses on the implementation of GPU-based high-performance graph algorithms, as well as on the statistical and machine learning analysis of human brain functional networks in a multi-site resting-state functional MRI database framework. He completed his Ph.D. degree in Physics in 2017 from Florida International University. Oswaldo is the first author of several peer-reviewed publications that have appeared in Neuroinformatics and Physical Review C journals, as well as in IEEE Big Data, IEEE IPDPS, International Conference on Parallel Processing, and IEEE BIBM conference proceedings.