ACTIVITY STATES IN HIERARCHICAL NETWORKS

**Relevant for Research Areas**

Neuroanatomy, animal experiments and human lesion studies have now converged in their view that brain networks are organized in multiple structural and functional hierarchies. Most strategies to interfere with brains by recording and/or stimulation operate at a mesoscopic scale of network organization. It is, therefore, important to improve our insight into the structural determinants of neuronal activity dynamics in healthy and dysfunctional brains at this scale. At the present time, only computational methods – large-scale numerical simulations of neuronal networks, enhanced by analytical approaches – can generate such an integrated understanding.

We have studied, how the detailed topology of a network in the brain determines its activity dynamics in terms of firing rates and pairwise and higher-order correlations, assuming linear interaction dynamics. Thereby, networks are conceived as a set of nodes linked together in a specific way (directed graph). Nodes are defined by either single neurons or neuronal populations. Axons, or axon bundles, and associated synapses determine the links between nodes. Nonlinear properties of neuronal integration could be accounted for using standard neuron models and characteristic network connectivity motifs. Specifically, in networks dominated by inhibition, external input provided by afferent connections or external stimulation is processed in surprisingly rich and biologically relevant ways. To better understand the properties of mass signals (EEG, ECoG or fMRI) that reflect multiple interacting neuronal populations in recordings, reduced mean-field models have been developed and analyzed.

Large-scale spiking neuronal network models, and their associated mean-field theory, represent a powerful toolset to gain a better theoretical understanding of the dynamics and function of brain networks with a hierarchical structure. It is fair to say that multi-scale neuronal network models have become an indispensable tool to support data analysis and interpretation, and to optimize the yield of experiments in fundamental brain research, and the efficiency of novel methods of therapeutical intervention in the diseased brain. The future success of the approach will depend on the availability of a flexible modeling and simulation framework that can account for micro-, meso- and macro-scale anatomical information.

**Publications in peer-reviewed journals**

Papers that acknowledge BrainLinks-BrainTools support are marked with an asterisk.

P1. *Deniz T, Rotter S. Joint statistics of strongly correlated neurons via dimensionality reduction. *Journal of Physics A: Mathematical and Theoretical* 50(25): 254002, 2017

P2. *Deniz T, Rotter S. Solving the two-dimensional Fokker-Planck equation for strongly correlated neurons. *Physical Review E* 95: 012412, 2017

P3. *Gallinaro JV, Rotter S. Associative properties of structural plasticity based on firing rate homeostasis in recurrent neuronal networks. *Scientific Reports* 8: 3754, 2018

P4. Jovanović S, Hertz J, Rotter S. Cumulants of Hawkes point processes. *Physical Review E* 91: 042802, 2015

P5. *Jovanović S, Rotter S. Interplay between graph topology and correlations of third order in spiking neuronal networks. *PLOS Computational Biology* 12(6): e1004963, 2016

P6. Kumar A, Cardanobile S, Rotter S, Aertsen A. The role of inhibition in generating and controlling Parkinson’s disease oscillations in the basal ganglia. *Frontiers in Systems Neuroscience* 5: 86, 2011

P7. *Lagzi F, Rotter S. A Markov model for the temporal dynamics of balanced random networks of finite size. *Frontiers of Computational Neuroscience* 8: 142, 2014

P8. *Lagzi F, Rotter S. Dynamics of competition between subnetworks of spiking neuronal networks in the balanced state. *PLOS ONE* 10(9): e0138947, 2015

P9. Pernice V, Staude B, Cardanobile S, Rotter S. How Structure Determines Correlations in Neuronal Networks. *PLOS Computational Biology* 7(5): e1002059, 2011

P10. Pernice V, Staude B, Cardanobile S, Rotter S. Recurrent interactions in spiking networks with arbitrary topology. *Physical Review E* 85: 031916, 2012

P11. Sadeh S, Cardanobile S, Rotter S. Mean-field analysis of orientation selectivity in inhibition-dominated networks of spiking neurons. *SpringerPlus* 3(1): 148, 2014

P12. *Sadeh S, Rotter S. Distribution of orientation selectivity in recurrent networks of spiking neurons with different random topologies. *PLOS ONE* 9(12): e114237, 2014

P13. *Sadeh S, Rotter S. Orientation selectivity in inhibition-dominated networks of spiking neurons: effect of single neuron properties and network dynamics. *PLOS Computational Biology* 11(1): E1004045, 2015

P14. *Sadeh S, Clopath C, Rotter S. Processing of feature selectivity in cortical networks with specific connectivity. *PLOS ONE* 10(6): e0127547, 2015

P15. *Sadeh S, Clopath C, Rotter S. Emergence of functional specificity in balanced networks with synaptic plasticity. *PLOS Computational Biology* 11(6): e1004307, 2015

P16. *Yim MY, Kumar A, Aertsen A, Rotter S. Impact of correlated inputs to neurons: Modeling observations from in vivo intracellular recordings. *Journal of Computational Neuroscience* 37(2): 293-304, 2014

**Unpublished manuscripts**

U1. *Lagzi F, Atay FM, Rotter S. Bifurcation analysis of the dynamics of interacting populations of spiking networks. *arXiv*, 2018

U2. *Merkt B, Schuessler F, Rotter S. Propagation of orientation selectivity in a spiking network model of layered primary visual cortex. *bioRxiv*, 2018

U3. *Lu H, Gallinaro J, Rotter S. Network remodeling induced by transcranial brain stimulation: A computational model of tDCS-triggered cell assembly formation. *Submitted*, 2018

U4. *Kordovan M, Rotter S. Systematic coarse graining of network dynamics. *Manuscript in preparation*, 2018

**Contributions to international conferences**

C1. Deniz T, Rotter S. Theory of Spike Correlation Asymmetry and Network Heterogeneity. Göttingen, Bernstein Conference 2014. www.bernstein-conference.de/2014

C2. Lagzi F, Rotter S. Nonlinear Stochastic Mean-Field Dynamics of Interacting Populations of Spiking Neurons. Göttingen, Bernstein Conference 2014. www.bernstein-conference.de/2014

C3. Sadeh S, Rotter S. Joint Representation of Ocularity, Color and Orientation Selectivity in a Mixing Model of Primary Visual Cortex. Maps 2014 – From Maps to Circuits: Models and Mechanisms for Generating Neural Connections. Edinburgh, UK, 28/29 July 2014. damtp.cam.ac.uk/user/eglen/maps2014/

C4. Sadeh S, Rotter S. Linear and nonlinear processing of visual information in rodent-like cortical networks. Areadne 2014 – Research in Encoding And Decoding of Neural Ensembles. Santorini, Greece, 25-29 June 2014. http://areadne.org/

C5. Deniz T, Rotter S. Solving the 2-dimensional Fokker-Planck equation for strongly correlated neurons (talk & tutorial). Junior Scientist Workshop on Theoretical Neuroscience. HHMI, Janelia Research Center, Ashburn, Virginia, USA. 25-30 September 2016. https://www.janelia.org/you-janelia/conferences/junior-scientist-workshop-theoretical-neuroscience

C6. Gallinaro J, Rotter S. Non-random connectivity of networks induced by homeostatic structural plasticity. Poster. Berlin, *Bernstein Conference 2018*, http://www.bernstein-conference.de/2018

C7. Gallinaro J, Rotter S. Associative properties of structural plasticity based on firing rate homeostasis. Talk. Berlin, *Bernstein Conference 2018*, http://www.bernstein-conference.de/2018

C8. Lagzi F, Atay FM, Rotter S. Bifurcation analysis of three interacting subnetworks of spiking neurons. Poster. Berlin, *Bernstein Conference 2018*, http://www.bernstein-conference.de/2018

C9. Merkt B, Schuessler F, Rotter S. Tuning Selectivity in Cortical Layers Results from Generic Connectome by Microcircuit-Level Processing. Poster. Berlin, *Bernstein Conference 2018*, http://www.bernstein-conference.de/2018

C10. Merkt B, Rotter S. Processing of non-homogeneous input by multi-population networks. Talk. Berlin, *Bernstein Conference 2018*, http://www.bernstein-conference.de/2018

C11. Tabarelli M, Rotter S. Input-output relations of inhibition-dominated networks with a 3-dimensional input ensemble. Poster. Berlin, *Bernstein Conference 2018*, http://www.bernstein-conference.de/2018