Many neural circuits shows correlated firing among neurons; these correlations have been shown to be important for the encoding and decoding of sensory information. 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. 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 student 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: 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. For more information see: https://www.smartnets-etn.eu/how-higher-order-correlations-shape-network-structure/

Postdoc position: The postdoc candidate will be involved in a computational project addressing how neurons efficiently synthesize and distribute proteins in order to ensure that these are readily available across all synapses, will analyze data and model synaptic plasticity changes in order to understand health and disease states computationally. This work is centered on computational tools and includes pen-and-paper calculations, data analysis, and numerical simulations and requires an interdisciplinary mindset. PhD position: The PhD candidate will be conducting circuit level data analysis and modeling of neural activity states. He/she will contribute to the development of machine learning algorithms to analyse imaging data or to distinguish different behavioral activity states. This work is centered on dynamical systems methods, data analysis and numerical simulations and requires an interdisciplinary mindset. Master students interested in conducting Master thesis research (6-12 months) related to the two projects above a welcome to apply.