Dynamics of neural networks with different motif distributions
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1
Heriot-Watt University, School of Mathematics and Computer Science, United Kingdom
Recently, several research fields underwent considerable advances thanks to the study of the networks underlying specific process or phenomena. Some of these studies report that 3-node motifs (small sub-networks contained within larger networks) could be linked with the function of specific biological networks (Milo, 2002).
The network model with structured nodes (SN model) has been recently introduced (Frisco, 2011) as an algorithm able to generate networks with specific features including the 3-node motif distribution (3NMD): the abundance of each 3-node motif in a network. We used the SN model to generate two networks, network 1 and network 2, each with 250 nodes and with different 3NMDs, shown in Figure 1 and Figure 2.
These two networks were then used to create two random recurrent neural networks (Dauce, 1998).
We observe the dynamics after applying a stimulus to the network. We used three different functions to apply the stimuli:
all: each neuron has an influence;
least x connected: the x neurons with the least outgoing connections have an influence;
most x connected: the x neurons with the most outgoing connections have an influence.
We run tests for x=20, x=50 and x=100.
Our analysis focused on the differences in the dynamics of the two networks depending on the stimuli functions. We observed whether or not a network has regular dynamics after a stimulus has been applied.
Before any stimuli is applied the dynamics of network 1 are regular in a few cases, while network 2 never has regular dynamics.
In general, network 1 is more likely than network 2 to have a regular dynamics after any type of stimuli is applied. This is summarised by Table 1.
When all nodes in the networks receive a stimulus, then in 88% of the tests network 1 has a regular dynamics while network 2 only 53%.
Network 1 has a regular dynamics independently from influencing the least or most connected nodes and the percentages of tests leading to regular dynamics are very close to each other when these functions are applied. We had expected the influence on the most connected nodes to lead to regular dynamics more frequently than the influence on the least connected nodes (this is indeed the case for network 2).
We also noticed that the increase in the number of influenced nodes (least or most connected) is not followed by a proportional increase in the number of networks having a regular dynamics.
The percentage of tests having a regular dynamics deriving from network 1 is always much higher than the ones deriving from network 2.
All this let us to conclude that 3NMD has a strong effect on dynamics.
References
Dauce, E., Quoy, M., Cessac, B., Doyon, B., and Samuelides, M. (1998) Self-organization and dynamics reduction in recurrent networks: stimulus presentation and learning. Neural Netw., 11:521–533.
Frisco, P. (2011) Network model with structured nodes. Physical Review E. accepted.
Milo, R., Shen-Orr, S., Itzkovitz, S., Kashtan, N., Chklovskii, D., and Alon, U. (2002) Network motifs: simple building blocks of complex networks. Science, 298(5594):824–827.
Keywords:
dynamical systems,
networks,
Neurons
Conference:
BC11 : Computational Neuroscience & Neurotechnology Bernstein Conference & Neurex Annual Meeting 2011, Freiburg, Germany, 4 Oct - 6 Oct, 2011.
Presentation Type:
Poster
Topic:
neurons, networks and dynamical systems (please use "neurons, networks and dynamical systems" as keywords)
Citation:
Govan
G and
Frisco
P
(2011). Dynamics of neural networks with different motif distributions.
Front. Comput. Neurosci.
Conference Abstract:
BC11 : Computational Neuroscience & Neurotechnology Bernstein Conference & Neurex Annual Meeting 2011.
doi: 10.3389/conf.fncom.2011.53.00190
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Received:
19 Aug 2011;
Published Online:
04 Oct 2011.
*
Correspondence:
Mr. Gordon Govan, Heriot-Watt University, School of Mathematics and Computer Science, Edinburgh, EH11 4AS, United Kingdom, gmg8@hw.ac.uk