scholarly journals Dynamics of a Large-Scale Spiking Neural Network with Quadratic Integrate-and-Fire Neurons

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Weijie Ye
Keyword(s):  
Neural Network ◽  
Large Scale ◽  
Field Model ◽  
Network Dynamics ◽  
Mean Field ◽  
Spiking Neural Network ◽  
Stable Limit ◽  
Mean Field Model ◽  
Integrate And Fire ◽  
The Mean

Since the high dimension and complexity of the large-scale spiking neural network, it is difficult to research the network dynamics. In recent decades, the mean-field approximation has been a useful method to reduce the dimension of the network. In this study, we construct a large-scale spiking neural network with quadratic integrate-and-fire neurons and reduce it to a mean-field model to research the network dynamics. We find that the activity of the mean-field model is consistent with the network activity. Based on this agreement, a two-parameter bifurcation analysis is performed on the mean-field model to understand the network dynamics. The bifurcation scenario indicates that the network model has the quiescence state, the steady state with a relatively high firing rate, and the synchronization state which correspond to the stable node, stable focus, and stable limit cycle of the system, respectively. There exist several stable limit cycles with different periods, so we can observe the synchronization states with different periods. Additionally, the model shows bistability in some regions of the bifurcation diagram which suggests that two different activities coexist in the network. The mechanisms that how these states switch are also indicated by the bifurcation curves.

scholarly journals Biologically realistic mean-field models of conductancebased networks of spiking neurons with adaptation

2018 ◽  
Author(s):  
Matteo di Volo ◽  
Alberto Romagnoni ◽  
Cristiano Capone ◽  
Alain Destexhe
Keyword(s):  
Large Scale ◽  
Field Model ◽  
Mean Field ◽  
Inhibitory Neurons ◽  
Activity Levels ◽  
Mean Field Model ◽  
Nonlinear Properties ◽  
Mean Field Models ◽  
The Mean

AbstractAccurate population models are needed to build very large scale neural models, but their derivation is difficult for realistic networks of neurons, in particular when nonlinear properties are involved such as conductance-based interactions and spike-frequency adaptation. Here, we consider such models based on networks of Adaptive exponential Integrate and fire excitatory and inhibitory neurons. Using a Master Equation formalism, we derive a mean-field model of such networks and compare it to the full network dynamics. The mean-field model is capable to correctly predict the average spontaneous activity levels in asynchronous irregular regimes similar to in vivo activity. It also captures the transient temporal response of the network to complex external inputs. Finally, the mean-field model is also able to quantitatively describe regimes where high and low activity states alternate (UP-DOWN state dynamics), leading to slow oscillations. We conclude that such mean-field models are “biologically realistic” in the sense that they can capture both spontaneous and evoked activity, and they naturally appear as candidates to build very large scale models involving multiple brain areas.

Performance Analysis of Work Stealing in Large-scale Multithreaded Computing

2021 ◽  
Vol 6 (2) ◽  
pp. 1-28
Author(s):  
Nikki Sonenberg ◽  
Grzegorz Kielanski ◽  
Benny Van Houdt
Keyword(s):  
Fixed Point ◽  
Large Scale ◽  
Field Model ◽  
Unique Fixed Point ◽  
Mean Field ◽  
Response Time Distribution ◽  
Mean Field Model ◽  
Work Stealing ◽  
Poisson Arrivals ◽  
The Mean

Randomized work stealing is used in distributed systems to increase performance and improve resource utilization. In this article, we consider randomized work stealing in a large system of homogeneous processors where parent jobs spawn child jobs that can feasibly be executed in parallel with the parent job. We analyse the performance of two work stealing strategies: one where only child jobs can be transferred across servers and the other where parent jobs are transferred. We define a mean-field model to derive the response time distribution in a large-scale system with Poisson arrivals and exponential parent and child job durations. We prove that the model has a unique fixed point that corresponds to the steady state of a structured Markov chain, allowing us to use matrix analytic methods to compute the unique fixed point. The accuracy of the mean-field model is validated using simulation. Using numerical examples, we illustrate the effect of different probe rates, load, and different child job size distributions on performance with respect to the two stealing strategies, individually, and compared to each other.

scholarly journals Dynamical Bridge Between Song Degradation and Neural Plasticity

2021 ◽  
Author(s):  
Jie Zang ◽  
Shenquan Liu
Keyword(s):  
Neural Plasticity ◽  
Field Model ◽  
Mean Field ◽  
Stable Limit Cycle ◽  
Bistable System ◽  
Stable Node ◽  
Stable Limit ◽  
Mean Field Model ◽  
Mean Field Equations ◽  
The Mean

Abstract High dimensionality and complexity are the main difficulties of the study over network dynamics. Recently, Wilten Nicola proposed the mean field theory to research the bifurcations that the full networks display. Here, we use his approach on the birdsong neural network. Our previous work has shown that AFP could adjust the synapse conductance of nucleus RA and change RA’s firing patterns, eventually leading to song degradation. To understand the dynamical principle behind this, we use a technique to reduce the RA network to a mean field model, in the form of a system of switching ordinary differential equations. Numerical results have shown that the mean field equations can qualitatively and quantitatively describe the behavior of nucleus RA. Based on the non-smooth bifurcation analysis of the mean field model, we determine that there is a subcritical-Andronov-Hopf bifurcation at a particular stimulation, which can explain the role of AFP during song degradation. The results indicate that we can see AFP’s adjustment in RA synapse conductance as the adjustment of initial value in the bistable system. More precisely, during song degradation, the mean field system would transform to a stable node (corresponding to distorted songs) rather than a stable limit cycle (corresponding to normal songs).

scholarly journals Biologically Realistic Mean-Field Models of Conductance-Based Networks of Spiking Neurons with Adaptation

2019 ◽  
Vol 31 (4) ◽  
pp. 653-680 ◽  
Author(s):  
Matteo di Volo ◽  
Alberto Romagnoni ◽  
Cristiano Capone ◽  
Alain Destexhe
Keyword(s):  
Large Scale ◽  
Field Model ◽  
Mean Field ◽  
Inhibitory Neurons ◽  
Activity Levels ◽  
Mean Field Model ◽  
Nonlinear Properties ◽  
Mean Field Models ◽  
The Mean

Accurate population models are needed to build very large-scale neural models, but their derivation is difficult for realistic networks of neurons, in particular when nonlinear properties are involved, such as conductance-based interactions and spike-frequency adaptation. Here, we consider such models based on networks of adaptive exponential integrate-and-fire excitatory and inhibitory neurons. Using a master equation formalism, we derive a mean-field model of such networks and compare it to the full network dynamics. The mean-field model is capable of correctly predicting the average spontaneous activity levels in asynchronous irregular regimes similar to in vivo activity. It also captures the transient temporal response of the network to complex external inputs. Finally, the mean-field model is also able to quantitatively describe regimes where high- and low-activity states alternate (up-down state dynamics), leading to slow oscillations. We conclude that such mean-field models are biologically realistic in the sense that they can capture both spontaneous and evoked activity, and they naturally appear as candidates to build very large-scale models involving multiple brain areas.

Single-Crystal Magnetic Properties of [Co(NH3)5(OH2)] [Cr(CN)6] Between 2 and 300 K

1992 ◽  
Vol 45 (11) ◽  
pp. 1899 ◽  
Author(s):  
PA Reynolds ◽  
CD Delfs ◽  
BN Figgis ◽  
B Moubaraki ◽  
KS Murray
Keyword(s):  
Ising Model ◽  
Field Model ◽  
Mean Field ◽  
Zero Field ◽  
Spin Orbit Coupling ◽  
Zero Field Splitting ◽  
Magnetic Exchange Interaction ◽  
Mean Field Model ◽  
Magnetic Exchange ◽  
The Mean

The magnetic susceptibilities along and perpendicular to the c axis (hexagonal setting) between 2.0 and 300 K at a magnetic field of 1.00 T, and the magnetizations at field strengths up to 5.00 T, are presented for single crystals of [Co(NH3)5(OH2)] [Cr(CN)6]. The results are interpreted in terms of zero-field splitting (2D) of the ground 4A2g term by spin-orbit coupling and of magnetic exchange interaction between the chromium atoms. The magnetic exchange is modelled as one of Ising or mean-field in type. The exchange is found to be quite small: J = -0.18(6) cm-1 if the Ising model is employed, and -0.03(1) cm-1 for the mean-field model. The model adopted for the exchange has a strong influence on the value of the parameter D obtained. When the Ising model is used D is deduced to be -0.28(9) cm-l; when the mean-field model is used D is -0.14(4) cm-l. The g-values deduced are in agreement with those from e.s.r. measurements at higher temperatures and do not depend on the exchange model. In any case, D is found to be sufficiently large that it must be considered in a polarized neutron diffraction experiment on the compound.

scholarly journals Phase diagram of the mean field model of simplicial gravity

1999 ◽  
Vol 542 (1-2) ◽  
pp. 413-424 ◽  
Author(s):  
P. Bialas ◽  
Z. Burda ◽  
D. Johnston
Keyword(s):  
Phase Diagram ◽  
Field Model ◽  
Mean Field ◽  
Mean Field Model ◽  
The Mean

A Phase Diagram for the Ice VI–VII–VIII Transitions

1998 ◽  
Vol 12 (08) ◽  
pp. 271-279 ◽  
Author(s):  
H. Yurtseven ◽  
S. Salihoğlu
Keyword(s):  
Phase Diagram ◽  
Phase Transitions ◽  
Field Model ◽  
Mean Field ◽  
Calculated Phase Diagram ◽  
Mean Field Model ◽  
Phase Line ◽  
Calculated Phase ◽  
The Mean ◽  
T Phase

In this study we obtain the P–T phase diagram for the ice VI–VII–VIII phase transitions by means of the mean field model developed here. We have fitted the experimentally measured P–T data to our phase line equations. Our calculated phase diagram describes adequately the observed behavior of the ice VI–VII–VIII phase transitions.

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