Max Planck Institute for Dynamics and Self-Organization -- Department for Nonlinear Dynamics and Network Dynamics Group
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Dr. Anna Levina

Projects: Self-Organized Criticality in the Activity Dynamics of Neural Networks, Complex Disordered Systems: Statistical Physics and Symbolic Computation
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CV: download


My previous research is highlighted on the project page.

Now I am working on the following projects:

Optimality of the critical systems.

This project I supervise as a B4 project of BCCN.

The greatest challenge in the studies of neuronal avalanches  is to prove, that they indeed lead to a certain optimality in  cortical networks.
I study in detail the properties of dynamic range, that so far was the most established measure of optimality. I show that there are examples where networks commonly attributed as sub- or supra-critical  attain the largest dynamic range and discuss under which conditions the dynamic range is indeed optimized near criticality.  I am also planning to use machine learning tasks to measure performance of the network and compare critical and extra-critical regimes.

On the other side it is important to show, that maintaining criticality does not preclude learning. I found that  combining criticality with even such a typical task as storing memory is not a trivial task. Together with Max Uhlig amd Michael J Herrmann I showed, that alternating Hebbian learning with the long-term homeostatic adaptation toward critical state allows for simultaneous memory storage and criticality. As the next step of investigation I will test whether for specific patterns (for example including  complicated temporal correlations) criticality of network can be beneficial.


Definition of criticality

Currently  there is no mathematically established way to define criticality for neuronal avalanches. The most widely spread  definition is based on the closeness of avalanche size distribution to the nearest power-law distribution,  or to the power-law distribution with the particular slope. Commonly, for  processes with the power-law slope of approximately -3/2, this definition will be corroborated by the assessment  of the branching ratio closeness to unity. The latter is based on the mathematical results for critical branching processes.   Recently scientists started to use also detrended fluctuation analysis, that does not allow to separate critical from near-critical distributions, but enables to indirectly measure self-affinity of the system. All these methods possess a large arbitrariness in the threshold selection, – they do not have a rigorous statistical methodology.

Therefore there is a real necessity to improve our understanding of what is so particular about the neuronal datasets and models that we call critical and what separates them from the rest of their respective families. This question is not easy to answer and I work in different complimentary directions, that should improve our comprehension of criticality.

Parts of this project are done in collaboration with Viola Priesemann


Self-organization of network structure

Structural inhomogeneities in synaptic efficacies have a strong impact on population response dynamics of cortical networks and are believed to play an important role in their functioning. However, little is known about how such inhomogeneities could evolve by means of synaptic plasticity. Together with F. Effenberger and J. Jost I studied  an adaptive model of a balanced neuronal network that combines two different types of plasticity, STDP and synaptic scaling. We showed that plasticity rules yield both long-tailed distributions of synaptic weights and of firing rates and, simultaneously, a highly connected subnetwork of driver neurons with strong synapses emerges.  

Now there are may open questions, starting from the scalability of our approach and the implementation of topographic initial network structure, to the possibility of guiding reorganization of the network to perform special tasks.

Selected Articles:
A. Levina, and J.M. Herrmann (2014).
The Abelian distribution
Stochastics and Dynamics 14(3):1450001. download file
M. Uhlig, A. Levina, T. Geisel, and J.M. Herrmann (2013).
Critical dynamics in associative memory networks.
Front. Comput. Neurosci. 7(87). download file
J. Nagler, A. Levina, and M. Timme (2011).
Impact of single links in competitive percolation
Nature Physics 7:265. download file download file
A. Levina, J.M. Herrmann, and T. Geisel (2009).
Phase transitions towards criticality in a neural system with adaptive interactions
Phys. Rev. Lett. 102(11):118110. download file
A. Levina, J.M. Herrmann, and T. Geisel (2007).
Dynamical synapses causing self-organized criticality in neural networks
Nature Physics 3:857-860. download file

Publications (chronological - click here to see all publications)