## Dynamics and estimation of large-scale spiking neuronal network models

Computations in neural circuits emerge from the interaction of many neurons. Although accurate single neuron models exist, little is known about the synaptic connectivity of large-scale circuits of neurons. However, recent experimental techniques enable recordings of the activity of thousands of neurons in parallel. Such data hold the promise that inferences about the underlying synaptic connectivity can be made. I will present two complementary approaches to gain insights into the collective dynamics of neural circuits.On the one hand, I will report on recent progress in the reconstruction of networks of 1000 simulated spiking neurons by maximum likelihood estimation of a generalized linear model (GLM), in which a million possible synaptic efficacies have to be determined. The work demonstrates that reconstructing the connectivity of thousands of neurons is feasible, and that hidden embedded subpopulations can be detected in the reconstructed connectivity.

On the other hand, spiking GLM's are a versatile class of single neuron models that can represent important features such as intrinsic stochasticity, refractoriness, and spike-frequency adaptation. For this class of models, I will present a new theory of population dynamics, which takes into account finite-size fluctuations and accurately describes the population-averaged neural activity in time, in response to arbitrary stimuli. Based on this theory, GLM network models with parameters extracted from data can be used to understand neural processing in realistic networks, and circuit-level information processing can be explained.