Interaction of neurobiological systems: dynamics and function

I entered neuroscience as an experimentalist, and began investigating cortical and subcortical interaction particularly in mice performing goal-directed tasks. I mostly employed locomotion in mice as a model system and examined the interaction of cortical, basal ganglia and brainstem circuitry in interrupting action and controlling it. The horizon goal is to dissect a motor interrupt system module in the brain which I hypothesize is key in switching action, and extends to interrupting and switching thoughts and emotions. My approach combined systems theory with a range of experimental techniques from optogenetics, to viral tracings, two-photon microscopy and extracellular single-unit recordings with cell-type specific photo-identification. My efforts also extended to engineering the recording and behavioral equipment myself, as well as developing surgical procedures and animal training techniques for my specific needs. The research insight into the basal ganglia and its rhythms also extended into understanding the mechanism of Deep Brain Stimulation for Parkinson's Disease primarily through biophysical modeling.

I am currently researching brain dynamics under anesthesia, delineating their evolution and underlying biophysical mechanism. Using a combination of biophysical modeling, systems theoretic insight and signal processing with a range of experiments in mice, rats and non-human primates, I aim to monitor and precisely control the level of unconsciousness of patients undergoing surgery.

My research interests generally span the interaction of neurobiological systems, the dynamics they generate and the implication of these dynamics on motor, cognitive, affective and arousal processes. I am guided by the principle that intricate complex brain dynamics emerge from interaction of simple systems, and it is through a fundamental understanding of the systems, their interaction motif and its evolution that we can understand brain function, and unlock our ability to control it. Through this, my goal is to develop neurobiologically-guided principles in mathematics and engineering that can best express the sought phenomena, design and execute experiments that verify and examine these principles in the brain to elucidate brain function, and leverage the uncovered experimental insight to refine these principles and be led to new ones. This endeavor allows for a good opportunity, whenever applicable, to engineer and deliver prototype systems for therapeutics.

Interaction of systems and emergent phenomena

In my doctoral work, I developed a framework to mathematically capture and study cascading and emergent phenomena. These phenomena are simplified as "a line of falling dominoes" but importantly they underlie crises in financial systems, spreads of social norms and rumors, cascaded failure in infrastructure and ecological consequences, to name a few. In my work, I devised a means to abstract the problem and relate emergent properties of an interconnected system to properties of its subsystems. In engineering, reducing a problem to something that is compositional is a very effective design and analysis strategy. By compositional we mean that when we build systems from smaller pieces, the properties of the smaller pieces extend to the big system. However in the setting of cascades, the lack of compositionality is the essence of the problem and we are forced to deal with it head on. How can we then study systems when necessarily "the whole is greater than the sum of its parts"? Building on a theory of interconnection reminiscent of the behavioral approach to systems theory, I developed and introduced a new notion of generativity, and its byproduct, generative effects, to capture these emerging phenomena. I then showed how to extract algebraic objects (e.g., vectors spaces) from the systems, that encode their generativity: their potential to generate new phenomena upon interaction. Those objects may then be used to link the properties of the interconnected system to its subcomponents. Such a link is executed through the use of exact sequences from commutative algebra.

In my doctoral work, I showed that diverse instances of cascade effects and emergent phenomena arise from the same mathematical structure. These instances cover models of opinion dynamics, to abstract models of cascading failures, to setups of interaction between memory, dynamics and subsystems. Throughout this work, I drew tools, techniques and insight from a mix of systems theory, order/lattice theory, category theory, formal languages, commutative algebra, homological algebra, (algebraic) topology and geometry and combinatorics.

Overall, this research direction opens up a fertile perspective to studying and understanding the interaction of systems and the effect that emerge from that interaction through insight, concepts and tools that have been largely absent when investigating emergent phenomena.

See the bibliography list for more details.