# Publications of Theory of multi-scale neuronal networks

## Selected publications of Theory of multi-scale neuronal networks

## Locking of correlated neural activity to ongoing oscillations

Population-wide oscillations are ubiquitously observed in mesoscopic signals of cortical activity. In these network states a global oscillatory cycle modulates the propensity of neurons to fire. Synchronous activation of neurons has been hypothesized to be a separate channel of signal processing information in the brain. A salient question is therefore if and how oscillations interact with spike synchrony and in how far these channels can be considered separate. Experiments indeed showed that correlated spiking co-modulates with the static firing rate and is also tightly locked to the phase of beta-oscillations. While the dependence of correlations on the mean rate is well understood in feed-forward networks, it remains unclear why and by which mechanisms correlations tightly lock to an oscillatory cycle. We here demonstrate that such correlated activation of pairs of neurons is qualitatively explained by periodically-driven random networks. We identify the mechanisms by which covariances depend on a driving periodic stimulus. Mean-field theory combined with linear response theory yields closed-form expressions for the cyclostationary mean activities and pairwise zero-time-lag covariances of binary recurrent random networks.
**Kühn T., Helias M. PLoS Comput Biol 13(6): e1005534 (2017): Locking of correlated neural activity to ongoing oscillations …**

## Integration of Continuous-Time Dynamics in a Spiking Neural Network Simulator

Contemporary modeling approaches to the dynamics of neural networks include two important classes of models: biologically grounded spiking neuron models and functionally inspired rate-based units. We present a unified simulation framework that supports the combination of the two for multi-scale modeling, enables the quantitative validation of mean-field approaches by spiking network simulations, and provides an increase in reliability by usage of the same simulation code and the same network model specifications for both model classes.
**Hahne J., Dahmen D., Schuecker J., Frommer A., Bolten M., Helias M., Diesmann M. Front. Neuroinform. 11:34. (2017): Integration of Continuous-Time Dynamics in a Spiking Neural Network Simulator …**

## Fundamental Activity Constraints Lead to Specific Interpretations of the Connectome

The continuous integration of experimental data into coherent models of the brain is an increasing challenge of modern neuroscience. Such models provide a bridge between structure and activity, and identify the mechanisms giving rise to experimental observations. Nevertheless, structurally realistic network models of spiking neurons are necessarily underconstrained even if experimental data on brain connectivity are incorporated to the best of our knowledge. Guided by physiological observations, any model must therefore explore the parameter ranges within the uncertainty of the data.
**Schuecker J., Schmidt M., van Albada SJ., Diesmann M., Helias M. PLoS Comput Biol 13(2): e1005179 (2017): Fundamental Activity Constraints Lead to Specific Interpretations of the Connectome …**

## Identifying Anatomical Origins of Coexisting Oscillations in the Cortical Microcircuit

Oscillations are omnipresent in neural population signals, like multi-unit recordings, EEG/MEG, and the local field potential. They have been linked to the population firing rate of neurons, with individual neurons firing in a close-to-irregular fashion at low rates. Using a combination of mean-field and linear response theory we predict the spectra generated in a layered microcircuit model of V1, composed of leaky integrate-and-fire neurons and based on connectivity compiled from anatomical and electrophysiological studies. The model exhibits low- and high-γ oscillations visible in all populations. Since locally generated frequencies are imposed onto other populations, the origin of the oscillations cannot be deduced from the spectra. We develop an universally applicable systematic approach that identifies the anatomical circuits underlying the generation of oscillations in a given network.
**Bos H., Diesmann M., Helias M. PLoS Comput Biol 12(10): e 1005132 (2016): Identifying Anatomical Origins of Coexisting Oscillations in the Cortical Microcircuit …**

## Correlated Fluctuations in Strongly Coupled Binary Networks Beyond Equilibrium

Randomly coupled Ising spins constitute the classical model of collective phenomena in disordered systems, with applications covering glassy magnetism and frustration, combinatorial optimization, protein folding, stock market dynamics, and social dynamics. The phase diagram of these systems is obtained in the thermodynamic limit by averaging over the quenched randomness of the couplings. However, many applications require the statistics of activity for a single realization of the possibly asymmetric couplings in finite-sized networks. Examples include reconstruction of couplings from the observed dynamics, representation of probability distributions for sampling-based inference, and learning in the central nervous system based on the dynamic and correlation-dependent modification of synaptic connections.
**Dahmen D., Bos H., Helias M. Phys. Rev. X 6:031024. (2016): Correlated Fluctuations in Strongly Coupled Binary Networks Beyond Equilibrium …**