# (1) Computational neurobiology

**[PIs: ****Amunts****, ****Briggman****, ****Griebel****, ****Kerr****, ****Klein****, ****Lippert****, ****Luu****, ****Memmesheimer****, ****Schweitzer****]**

Computational neurobiology aims to understand how millions of nerve cells in complex networks collectively perform computations that underlie behavior linking processes across multiple scales: How do cellular mechanisms give rise to the dynamics of spiking activity in neural circuits? How does these dynamics implement computations, which allow animals to perceive and interact with the external world? While enormous progress has been made in defining structure and function of neural circuits from subcellular (e.g. microscopy) to macro-cellular (e.g. brain atlas) scales, these efforts still do not allow for a direct link between neural activity and behavior. To achieve this goal, it is rather necessary to quantitatively assess neural activity, computation and - at best - complex behavior simultaneously. We have developed experimental assays for studying animals which are engaged in complex behaviors. This includes advanced optical tools for precise tracking behavior, sensory inputs and neural activity in freely moving animals, together with optical and genetic tools for interrogation and reversible manipulation of cellular activity in behaving animals. Processing, analyzing and visualizing these data will require advanced computer-vision algorithms for precisely tracking animal behavior, statistical methods for extracting models of behavior from observational data, and mathematical techniques for reconstructing information about cellular activity from fluorescence measurements obtained with optical imaging methods. In our animal models, we will also constrain models of neural computation underlying animal behavior. Recurrently connected neural networks exhibit rich temporal dynamics implying an expressive computational repertoire with powerful properties. Understanding these computational properties is critical for biological and computational neural networks. We therefore will develop mathematical theories for understanding distributed computations in recurrent biological neural networks thereby bridging between the level of single neurons and neural networks and the level of behavior. We envisage a bidirectional inspiration: Machine learning algorithms will be used to understand biological neural networks and insights from biological neural networks will inspire the development of new machine learning techniques. E.g., an important behavior is mental exploration, such as to plan future paths in spatial navigation. Recent experimental results suggest that the brain uses specific sampling and integration techniques to compute optimal paths. In a similar way, integrals over paths and lattices are computed utilizing highly refined algo-rithms in RU-A. Collaboratively, algorithms used for computing the related quantities in the brain will be explored. Moreover, we will go beyond data mining of experimental data. Bayesian statistical methods for constraining mathematical models and simulations of neural dynamics obtained by experimental data will be developed. We also will build synergies with the theme on stochastic methods, as state-of-the art Bayesian approaches utilize Hamiltonian Monte Carlo methods overlapping with computational methods in QCD simulations.