The goal of this work is to identify the nature of computations carried out by specific parts of the brain. The approach is to combine theory and constraints provided by the structure and function of neural circuits to describe the mathematical operations performed by structures such as the primary visual cortex. The theories that result always make specific predictions that can be tested by comparison with experimental observations.
One important set of constraints arises from the fact that the vertebrate brain has a scalable architecture, and clues about the nature of computations used by the brain are contained in the laws that govern brain scaling. An important part of the program, then, is to determine experimentally the scaling laws to which neural circuits conform, and to understand the computational significance of these laws. Scaling laws - such as the rules that govern axon arbors when they are made larger - are established first in fish (fish brains, like the whole fish, continue to grow larger throughout life), and then extended to mammals.
The approach used generally is not modeling but rather theory more in the style of physics where general properties of the system are used to determine its behavior. In biology, every system has to carry out a particular job, and general properties must be derived from insights into how the system does what it has evolved to do. One must, then, identify properties that are optimized or conserved, and use these properties to make quantitative predictions about the system's behavior. An example of a theory of this sort would be one in which the receptive field structure of, say, retinal ganglion cells is derived from the requirement that the receptive fields cover the visual space smoothly in spite of some randomness in the growth of dendritic arbors.
The long range goal of our laboratory is to understand the computational resources of brains from the biophysical to the systems levels. The central issues being addressed are how dendrites integrate synaptic signals in neurons, how networks of neurons generate dynamical patterns of activity, how sensory information is represented in the cerebral cortex, how memory representations are formed and consolidated during sleep, and how visuo-motor transformations are adaptively organized. New techniques have been developed for modeling cell signaling using Monte Carlo methods (MCell) and the blind separation of brain imaging data into functionally independent components (ICA).