Department of Physics
University of California, Santa Barbara
Network Architecture and Predictive Dynamics of Brain Systems
The mathematical study of complex systems facilitates critical insights into real-world phenomena. While a plethora of theoretical and analytical tools are available to support this study, we focus on recent developments in statistical mechanics and network theory that together provide a flexible framework in which to characterize the organization of systems composed of many interacting parts. At the interdisciplinary boundary between statistical physics, applied mathematics, and neuroscience, we study the human brain as a network of cortical areas connected by structural or functional highways along which information propagates. Data acquired from non-invasive neuroimaging techniques has been used to demonstrate that brain network structure varies between individuals, can be linked to cognitive ability (e.g., our IQ), displays altered patterns in disease states like schizophrenia, and changes over time. A mathematical assessment of these changes enables the identification of dynamic signatures (like flexibility) that predict of cognitive behaviors (like learning), facilitating a direct feedback loop between theory and experiment. Using these approaches, we can begin to determine fundamental organizational principles of both underlying brain structure and its functional dynamics. In addition to understanding phenomena specific to the human brain, these studies facilitate the examination of more general questions about the relationships between system organization – both static and dynamic – and performance, as well as the influence of external constraints (e.g., energetic or spatial) on that organization.