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Impacts of clustering on noise-induced spiking regularity in the excitatory neuronal networks of subnetworks.

Li H, Sun X, Xiao J - Front Comput Neurosci (2015)

Bottom Line: With the obtained simulation results, we find that spiking regularity of the neuronal networks has little variations with changing of R and S when M is fixed.However, cluster number M could reduce the spiking regularity to low level when the uniform neuronal network's spiking regularity is at high level.Combined the obtained results, we can see that clustering factors have little influences on the spiking regularity when the entire energy is fixed, which could be controlled by the averaged coupling strength and the averaged connection probability.

View Article: PubMed Central - PubMed

Affiliation: School of Science, Beijing University of Posts and Telecommunications Beijing, China.

ABSTRACT
In this paper, we investigate how clustering factors influent spiking regularity of the neuronal network of subnetworks. In order to do so, we fix the averaged coupling probability and the averaged coupling strength, and take the cluster number M, the ratio of intra-connection probability and inter-connection probability R, the ratio of intra-coupling strength and inter-coupling strength S as controlled parameters. With the obtained simulation results, we find that spiking regularity of the neuronal networks has little variations with changing of R and S when M is fixed. However, cluster number M could reduce the spiking regularity to low level when the uniform neuronal network's spiking regularity is at high level. Combined the obtained results, we can see that clustering factors have little influences on the spiking regularity when the entire energy is fixed, which could be controlled by the averaged coupling strength and the averaged connection probability.

No MeSH data available.


Spatiotemporal patterns of the clustered neuronal networks for different cluster numberM. (A–C)g = 0.004; (D–F)g = 0.01; (G–I)g = 0.025. Here D = 0.015, R = 20, and S = 30.
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Figure 5: Spatiotemporal patterns of the clustered neuronal networks for different cluster numberM. (A–C)g = 0.004; (D–F)g = 0.01; (G–I)g = 0.025. Here D = 0.015, R = 20, and S = 30.

Mentions: From this subsection, we begin to discuss effects of clusterings on the neuronal networks' spiking regularity. Firstly, we investigate how the cluster number M influents it. Here, the ratio R = pin∕pout is set as 20 and the ratio S = gin∕gout is set as 30. Figure 4 exhibits dependence of the spiking regularity λ on cluster number M for three different coupling strength g. As discussed in the above subsection, the uniform neuronal networks' spiking regularity is lower when g = 0.004 and 0.025, while they could take almost highest spiking regularity when the coupling strength g is optimal, for example g = 0.01 when the noise intensity D = 0.015. From Figure 4, we can see that when the neuronal network has clustered structures, the spiking regularity measured by λ decreases with M for g = 0.01, and it does not change too much for g = 0.004 and 0.025. In order to observe the dependence of spiking regularity on M clearly, nine spatiotemporal patterns for three different values of M with g = 0.004, 0.01, and 0.025 are presented in the Figure 5, respectively. In the Figure 5, M is taken as 5 for Figures 5A,D,G, 10 for Figures 5B,E,H, and 20 for Figures 5C,F,I. For g = 0.004 and 0.025, the interspike intervals of each neuron observed from the corresponding spatiotemporal patterns shown by the Figures 5A–C,G–I are always irregular no matter what value of M takes. It indicates the clustered neuronal networks' spiking regularity always stay at lower levels, i.e., M has little influences on the spiking regularity in these cases. For g = 0.01, with increasing of clustering number M, the interspike intervals of each neuron change from regular to irregular as exhibited by Figures 3B, 5D–F, which indicates decreasing of spiking regularity of the clustered neuronal network. With these obtained results, we can see that the cluster number M could have some influences on the spiking regularity just when the uniform neuronal networks are at high levels (rf. g = 0.01). Furthermore, compared the spatiotemporal patterns exhibited in Figure 3 with the corresponding ones shown in Figure 5, we can see that the spatiotemporal patterns are split into more and more stripes with increasing of clustering number M. Here, we take Figures 3B, 5D–F with g = 0.01 as examples. Compared with Figure 3, we can clearly see five strips in Figure 5D where M = 5. And with M increases further to 10 and 20, the strips in the spatiotemporal patterns increase to 10 and 20 correspondingly, as shown in Figures 5E,F. In fact, every strip region indicates one cluster. Because inter-coupling strength is large enough and larger than intra-coupling strength, neurons inside each cluster are synchronized with each other but not synchronized with other neurons from other clusters. This is why we can clearly observe strips in Figures 5D–F.


Impacts of clustering on noise-induced spiking regularity in the excitatory neuronal networks of subnetworks.

Li H, Sun X, Xiao J - Front Comput Neurosci (2015)

Spatiotemporal patterns of the clustered neuronal networks for different cluster numberM. (A–C)g = 0.004; (D–F)g = 0.01; (G–I)g = 0.025. Here D = 0.015, R = 20, and S = 30.
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Figure 5: Spatiotemporal patterns of the clustered neuronal networks for different cluster numberM. (A–C)g = 0.004; (D–F)g = 0.01; (G–I)g = 0.025. Here D = 0.015, R = 20, and S = 30.
Mentions: From this subsection, we begin to discuss effects of clusterings on the neuronal networks' spiking regularity. Firstly, we investigate how the cluster number M influents it. Here, the ratio R = pin∕pout is set as 20 and the ratio S = gin∕gout is set as 30. Figure 4 exhibits dependence of the spiking regularity λ on cluster number M for three different coupling strength g. As discussed in the above subsection, the uniform neuronal networks' spiking regularity is lower when g = 0.004 and 0.025, while they could take almost highest spiking regularity when the coupling strength g is optimal, for example g = 0.01 when the noise intensity D = 0.015. From Figure 4, we can see that when the neuronal network has clustered structures, the spiking regularity measured by λ decreases with M for g = 0.01, and it does not change too much for g = 0.004 and 0.025. In order to observe the dependence of spiking regularity on M clearly, nine spatiotemporal patterns for three different values of M with g = 0.004, 0.01, and 0.025 are presented in the Figure 5, respectively. In the Figure 5, M is taken as 5 for Figures 5A,D,G, 10 for Figures 5B,E,H, and 20 for Figures 5C,F,I. For g = 0.004 and 0.025, the interspike intervals of each neuron observed from the corresponding spatiotemporal patterns shown by the Figures 5A–C,G–I are always irregular no matter what value of M takes. It indicates the clustered neuronal networks' spiking regularity always stay at lower levels, i.e., M has little influences on the spiking regularity in these cases. For g = 0.01, with increasing of clustering number M, the interspike intervals of each neuron change from regular to irregular as exhibited by Figures 3B, 5D–F, which indicates decreasing of spiking regularity of the clustered neuronal network. With these obtained results, we can see that the cluster number M could have some influences on the spiking regularity just when the uniform neuronal networks are at high levels (rf. g = 0.01). Furthermore, compared the spatiotemporal patterns exhibited in Figure 3 with the corresponding ones shown in Figure 5, we can see that the spatiotemporal patterns are split into more and more stripes with increasing of clustering number M. Here, we take Figures 3B, 5D–F with g = 0.01 as examples. Compared with Figure 3, we can clearly see five strips in Figure 5D where M = 5. And with M increases further to 10 and 20, the strips in the spatiotemporal patterns increase to 10 and 20 correspondingly, as shown in Figures 5E,F. In fact, every strip region indicates one cluster. Because inter-coupling strength is large enough and larger than intra-coupling strength, neurons inside each cluster are synchronized with each other but not synchronized with other neurons from other clusters. This is why we can clearly observe strips in Figures 5D–F.

Bottom Line: With the obtained simulation results, we find that spiking regularity of the neuronal networks has little variations with changing of R and S when M is fixed.However, cluster number M could reduce the spiking regularity to low level when the uniform neuronal network's spiking regularity is at high level.Combined the obtained results, we can see that clustering factors have little influences on the spiking regularity when the entire energy is fixed, which could be controlled by the averaged coupling strength and the averaged connection probability.

View Article: PubMed Central - PubMed

Affiliation: School of Science, Beijing University of Posts and Telecommunications Beijing, China.

ABSTRACT
In this paper, we investigate how clustering factors influent spiking regularity of the neuronal network of subnetworks. In order to do so, we fix the averaged coupling probability and the averaged coupling strength, and take the cluster number M, the ratio of intra-connection probability and inter-connection probability R, the ratio of intra-coupling strength and inter-coupling strength S as controlled parameters. With the obtained simulation results, we find that spiking regularity of the neuronal networks has little variations with changing of R and S when M is fixed. However, cluster number M could reduce the spiking regularity to low level when the uniform neuronal network's spiking regularity is at high level. Combined the obtained results, we can see that clustering factors have little influences on the spiking regularity when the entire energy is fixed, which could be controlled by the averaged coupling strength and the averaged connection probability.

No MeSH data available.