Research Interests

I am interested in using mathematical modeling to explore problems in neuroscience and propose plausible mechanisms underlying biological phenomena that may not be uncovered through experiments. Some topics include:

Neuronal Networks

Drawing by Santiago Ramón y Cajal, 1900. 
The cerebral cortex is similar to a garden filled with innumerable trees, the pyramidal cells, which can multiply their branches thanks to intelligent cultivation, send their roots deeper, and produce more exquisite flowers and fruits every day.

Modeling the human brain is an exciting and challenging endeavor due to the fact that it contains over 80 billion neurons, the connections of which are not well known and often hard to measure. As a result, there is a great need for modeling to offer insight into the underlying physiology and network dynamics. I use detailed modeling of neuronal networks for several purposes:

  • to investigate mechanisms underlying the development of orientation preference maps in the visual cortex, including the plasticity of both chemical synapses and electrical junctions. 
  • to understand how electrical connectivity among neurons in the adult prefrontal cortex affects network synchrony and oscillations

More details on projects involving neuronal network modeling

Mechanics of pain processing

The pain processing pathway in humans involves many areas, including the skin, spinal cord, midbrain, and cortex. How these areas work together to generate a painful experience still remains unclear. Since painful signals are first processed by neurons in the spinal cord, I work on models that interpret signals from the skin and process them for transmission to the cortex. This spinal-cord model is used to:

  • investigate the underlying daily modulation of pain sensitivity
  • uncover mechanisms underlying the efficacy of spinal cord stimulation in eliminating chronic pain
  • study the effect of neuronal injuries on pain processing

More details on projects involving pain processing

Data analysis of crime in Santa Monica

This work began at an AMS-MRC workshop on agent-based modeling with a very fun group of people. Given a comprehensive dataset of crimes committed in the Santa Monica area, the project aims to understand and predict trends in crime. In particular, we are interested in questions concerning the potential effect political and social events may have on different types of crimes and their locations.