This week’s image is taken from a study of Joint statistics of strongly correlated neurons via dimensionality reduction as part of the *Modelling and inference in the dynamics of complex interaction networks* special issue of Journal of Physics A: Mathematical and Theoretical.

The relative timing of action potentials in neurons recorded from local cortical networks often shows a non-trivial dependence, which is then quantified by cross-correlation functions. Theoretical models emphasize that such spike train correlations are an inevitable consequence of two neurons being part of the same network and sharing some synaptic input. For non-linear neuron models, however, explicit correlation functions are difficult to compute analytically, and perturbative methods work only for weak shared input.

In order to treat these strong correlations, Taşkın Deniz and Stefan Rotter suggest an alternative non-perturbative method.

Joint 2D membrane potential distribution of simulated neuron dynamics is compared to the joint distribution computed with the singular value decomposition method, demonstrating either heterogeneity in intrinsic parameters or in input rate. The results are presented for a range of four asymmetric parameters. From Taşkın Deniz and Stefan Rotter 2017 *J. Phys. A: Math. Theor.* **50** 254002 Copyright IOP Publishing.

The figure itself shows the important demonstration that the authors’ method predicts joint membrane potential distributions to a good extent.

Taşkın Deniz and Stefan Rotter work at the Bernstein Center Freiburg and Faculty of Biology, University of Freiburg.

**Read More: Joint statistics of strongly correlated neurons via dimensionality reduction**

**Special issue: Modelling and inference in the dynamics of complex interaction networks **

**Topical Review: Spatiotemporal dynamics of continuum neural fields**

This work is licensed under a Creative Commons Attribution 3.0 Unported License

Front and article image and quote taken from Taşkın Deniz and Stefan Rotter 2017 *J. Phys. A: Math. Theor.* **50** 254002, © IOP Publishing, All Rights Reserved.

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Categories: Journal of Physics A: Mathematical and Theoretical

Tags: Image of the week, Mathematical Model, Mathematical physics, Networks, Neurons