COMPLEX SYSTEMS SEMINAR<br>Network Architecture and Predictive Dynamics of Brain Systems

The study of complex systems poses significant mathematical
challenges but can simultaneously provide an increased mechanistic
understanding of real-world system function. I focus on recent
developments in network science that have provided methods to
characterize the organization and dynamics of systems that are
composed of many interacting parts. At the interdisciplinary boundary
between applied mathematics, statistical physics, and neuroscience, 
I 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
demonstrated that brain network structure varies between individuals,
can be linked to our IQ and cognitive abilities, displays altered
patterns in disease states like schizophrenia, and changes over time.
A mathematical assessment of these dynamics enables the identification
of network signatures that predict individual differences in cognitive
behaviors such as 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. Moreover, these results
lay the groundwork for statistical approaches to predict individual
brain responses to injury, disease, and clinical interventions, that
could enable the construction of personalized therapeutics,
diagnostics, and biomarkers for monitoring disease progression and
rehabilitation. 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 energetic or spatial constraints on that organization. In
ongoing work, we seek to link brain network dynamics with smaller
scale genetic drivers and larger scale social structures to build a
better understanding of the biophysical constraints on and neural
mechanisms of human decision making and their implications for a
statistical mechanics of human collective phenomena.