Research

Our current work …

is focused on the mathematics, physics, and engineering of structure-function dynamics in spatial-temporal geometric networks in the brain. We want to understand how the shape and and signaling dynamics of individual neurons and astrocytes, the connectivity and geometry of networks of neurons, and networks of interacting brain regions produce emergent properties that allow the brain to learn, compute, and process information and data. We want to understand what changes in these processes in autism spectrum disorder. And how we can use mathematical models and algorithms derived from our understanding of the brain to build next generation machine learning and brain machine interfaces that can learn and adapt to their environments and new data without prior training. 

 
 
 

The scope of our research 

Computational neuroscience and biophysics. Mathematical and physical modeling and simulations of neural processes at molecular, cellular, and systems scales, for the purpose of understanding how structures in the brain represent and process information. We have had a particular focus on modeling the calcium signaling dynamics of astrocyte neural glial cells.

Theoretical neuroscience. Distinct from computational modeling and numerical simulations of the biophysics of neurobiology, we have a strong focus on the theoretical analysis of dynamic signaling in networks(i.e. models, theorems, and proofs that drive new kowledge and predictions). We are interested arriving at a deep understanding of neurophysiological dynamics.  

Neural derived machine learning algorithms and AI. We are leveraging our theoretical and computational work to develop neural derived models and algorithms for non-biological engineered systems. In particular, we are developing a fundamentally new machine learning architecture that will be able to learn without prior training or exposure to data. 

Applied nanotechnology. Our lab engaged in the development and use of nanotechnology to study and interface with the brain. In particular, we have previously worked on the development of self assembling nanotechnologies for neural regeneration, and the optimization of chemically functionalized quantum dots to achieve high resolution imaging of cellular structure and calcium dynamics.

Neural engineering. An extension of our nanotechnology work is development of nanoengineered neural technologies intended to interface with the brain and restore clinical function.  

Applications to neurological disorders. Much of our work is of direct clinical relevance, or is translational and intended to restore clinical function. We have published on traumatic spinal cord injury and reactive gliosis, Alzheimer's disease, retinal prosthesis, and currently have a strong interest in the systems neuroscience of autism spectrum disorder (ASD) and related neurodevelopmental disorders.