One of the most important questions in computational neuroscience is how the brain’s structural wiring gives rise to its functional patterns. In order to understand the relationship between brain structure and function, various computational approaches have been undertaken in the past, which primarily focused on predicting various functional markers, such as functional connectivity matrix obtained from functional magnetic resonance imaging or the frequency spectra obtained from magnetoencephalography or electroencephalography recordings. Most of them assumed that the functional activity markers remain static over time. However, recent neuroimaging studies indicate that the brain's functional activity does not remain static even while resting. The spatiotemporal pattern of this activity varies in different neurological diseases such as schizophrenia and autism, and in macro states such as resting and sleep states. Currently, the mechanism of these dynamics is unclear and various statistical and mathematical modeling approaches are being undertaken to investigate its biophysics and how it alters in different diseases and macro states.

In this workshop we have put together recent statistical and mathematical modeling efforts aimed towards understanding dynamic macroscopic functional activity. While statistical techniques are powerful in capturing these dynamics, they are unable to consider the biophysics of neural activity and therefore can only provide limited mechanistic insight. On the other hand, while biophysical mathematical modeling can enable exploring the underlying mechanism of the functional activity, they suffer from model parameter inference and identifiability issues. In this workshop, we will focus on both the approaches. We focus largely on graph-based macroscopic systems for this purpose, since at the macroscopic scale, brain regions interact with each other via long range projection fibers – a network organization that is best addressed using graph theory. Graph theory will play an increasingly important role in attempts to understand the massive amounts of data generated by large collaborative projects such as the Human Connectome Project. Graph theory is not currently included in training for neuroscientists with a background in biology, physiology or psychology; conversely, computational neuroscientists are steeped in fine-scale neuronal models but may be unfamiliar with how the more abstract graph theoretic approaches can be applied to characterize brain networks.

Rough syllabus sorted by themes

The talks in the proposed workshop are based on two themes: statistical data-driven approaches and mathematical modeling approaches. Together, these themes will provide the audience with a broad overview of various techniques that can be used to investigate brain functional activity.

Desired learning outcomes

Upon completing this workshop, participants will understand:

Target audience

This workshop will provide attendees with detailed knowledge of the area that spans fundamental concepts through to advanced applications. It is thus suitable for people with varying levels of experience. Graph theoretic analysis of neuroscientific data is inherently interdisciplinary, and provides a unitary framework that transcends measurement techniques, resolution scales and different levels of complexity of the mathematical approaches. The presented integrated program is likely to be helpful in providing a comprehensive understanding of the field.

Our target audience includes neuroscientists with a background in the biological or psychological sciences with some prior exposure to graph theory, and individuals with a more quantitative computational background who have knowledge of neuronal models and are interested in how graph theory can be applied to characterize neural networks.