Many neural circuits shows correlated firing among neurons; these correlations have been shown to be important for the encoding and decoding of sensory information^{[11]}. While most work has addressed correlations between pairs of neurons, recently, an increasing number of experimental studies have characterized Higher-Order spiking Correlations (HOCs) in several brain areas^{[12]}. Theoretical work has also addressed the importance of higher-order correlations (HOCs) on the firing of a postsynaptic neuron on circuit function and coding, and on the synchronous firing and the distribution of activity in a neuronal pool. However, the functional significance of such HOC for synaptic plasticity remains poorly understood. The ESR in this project will study the role of these HOCs in how they shape plasticity in different network architectures. Previously, we have proposed and analyzed a model in feedforward networks, where plasticity depends on spike triplets^{[13]}: sets of three spikes (triplets) are used instead of pairs to induce synaptic potentiation and depression. While important for the propagation of neural activity, feedforward circuits are unlike the recurrent structure of the neocortex. Therefore, we would like to understand how these HOC and learning rules shape network connectivity in recurrent networks.

We propose a theoretical analysis involving the extension of Hawkes processes in mathematics to neural networks where different combinations of spikes (pairs and triplets) interact to drive plasticity. In addition to developing rigorous mathematical frameworks, this theory will enable us to relate measured correlations in the activity that drive plasticity to the selective potentiation and depression of specific connectivity motifs in real biological networks recorded experimentally (for e.g. synfire chains, propagating ensembles). Thus, we would be able to predict the possible network structures emerging based on different plasticity rules, which can be related to functional connectivity characterized through correlations measured in experimental data. The mathematical analysis will be accompanied with numerical simulations and data analysis from collaborating partners to test the theoretical predictions.

^{[11]}Latham PE, Nirenberg S (2005). J Neurosci 25(21):5195-206.

^{[12]}Ohiorhenuan IE, et al. (2010). Nature 466(7306):617-621.

^{[13]}Gjorgjieva J, et al. (2011). Proc Natl Acad Sci USA. 29;108(48):19383-8.

**Expected Results:**

1. To develop a rigorous mathematical framework for how higher-order correlations shape plasticity in recurrent networks.

2. To determine the contribution of different connectivity motifs in the emergence of different network structures.

3. To determine which network structures predicted by the theory are encountered in biological data.

**Planned secondment(s):**

1. Philip Laserstein, MathWorks, M15-20: develop fast and efficient simulation frameworks of modeling plasticity

2. Sorbonne Uni, Georges Debrégeas, M27-29: obtain experimental data to test theoretical predictions

**Enrolment in Doctoral degree(s): **You will be enrolled at the Graduate School of Life Sciences at the Technical University of Munich.