# Large Deviations, Dynamics and Phase Transitions in Large Stochastic and Disordered Neural Networks

@article{Cabana2013LargeDD, title={Large Deviations, Dynamics and Phase Transitions in Large Stochastic and Disordered Neural Networks}, author={Tanguy Cabana and J. Touboul}, journal={Journal of Statistical Physics}, year={2013}, volume={153}, pages={211-269} }

Neuronal networks are characterized by highly heterogeneous connectivity, and this disorder was recently related experimentally to qualitative properties of the network. The motivation of this paper is to mathematically analyze the role of these disordered connectivities on the large-scale properties of neuronal networks. To this end, we analyze here large-scale limit behaviors of neural networks including, for biological relevance, multiple populations, random connectivities and interaction… CONTINUE READING

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- 2018

- 20
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- 34
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#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 56 REFERENCES

Neural networks and physical systems with emergent collective computational abilities

- Computer Science
- 1999

- 3,347
- PDF

Excitatory and inhibitory interactions in localized populations of model neurons.

- Biology, Medicine
- 1972

- 2,706
- Highly Influential
- PDF

Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?

- Mathematics, Computer Science
- 2006

- 6,042
- PDF

Dynamics of Sparsely Connected Networks of Excitatory and Inhibitory Spiking Neurons

- Medicine, Computer Science
- 2004

- 1,302
- PDF

A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue

- Mathematics, Medicine
- 2004

- 1,247