Our work is on the nonlinear dynamics of neurons, neural networks, and neural populations. These dynamics are beautiful, and are richly varied from setting to setting – at times governed by mechanisms we can distill and explain and at times eluding our best analytical tools. Beyond explaining the emergent dynamics of neural circuits, we want to understand how they encode and make decisions about the sensory world. Making progress on these twin problems requires a range of perspectives and methods. We delight in collaboration with fellow theorists of many different backgrounds, and with cognitive neuroscientists, clinicians, and electrophysiologists. Our methods blend data analysis, dynamical systems, stochastic processes, and information theory – and treat neural dynamics occurring on a number of spatial and temporal scales.

**Below is a quick taste of several projects currently underway; we wrote this SIAM News article with another view. **

**For more, please check out this summary of our ongoing and recent research!**

## COOPERATIVE NEURAL DYNAMICS AND CODING

On the left is a schematic that typifies almost any biological neural network: cell pairs receive overlapping inputs, leading to correlated spiking. The transfer of correlated inputs into correlated spikes is strongly modulated by the nonlinear dynamics of neural spike generation. As a consequence, overlapping input can lead to rich patterns of coooperative neural firing across neural populations, as shown on the right. This can have major consequences for levels of encoded information.

Of course, the pictures above are just the tip of the iceberg. Real circuits produce cooperative firing across whole populations of cells, and these cells are connected with rich architectures. Our work on the dynamics of neural correlations and their impact on coding is in collaboration with Fred Rieke, Jaime de la Rocha, Brent Doiron, Kreso Josic, and Alex Reyes -- and within our group, Nick Cain, Yu Hu, Natash Cayco-Gajic, and David Leen are currently pursuing these topics.