July 2007 - July 2014

**How does electrical activity in neuronal circuits give rise to intelligent behavior? To answer this question, we are pursuing two synergistic research directions.**

First, we are reconstructing vertebrate and invertebrate wiring diagrams from electron microscopical data. Second, we are developing a theory of neuronal computation. Our interdisciplinary approach takes advantage of recent advances in applied mathematics and statistical learning theory as well as optimization theory. We believe that progress in both directions will enable us to map the components of neuronal circuits onto the mathematical steps of computational algorithms.

## Research

Our brain is a network of 10^11 neurons, each making synapses with 10^4 others. While each neuron's output is a relatively stereotypical computation on its inputs, the network is capable of highly sophisticated behavior.

How does such a distributed system of relatively simple components compute? We address this question by reconstructing the network's wiring diagram and developing the theory of neuronal computation.

Wiring diagram reconstruction, also known as connectomics, is a challenging problem because identification of synapses requires few-nanometer resolution resulting in terapixel data sets. As manual analysis of such data sets is impossible, we are developing automated algorithms for circuit reconstruction using computer vision and machine learning. Our reconstruction focuses on fly circuits underlying vision.

What kind of mathematics is needed to describe neuronal computation? Many aspects of brain architecture, such as overcompleteness and sparseness, point at sparse redundant representations as lingua franca of the brain. We are mapping mathematical algorithms involving sparse representations onto known brain circuits.