A mean field model of work stealing in large-scale systems

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.

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Cluster mean-field theory accurately predicts statistical properties of large-scale DNA methylation patterns

10.1101/2021.09.03.458837 ◽

2021 ◽

Author(s):

Lyndsay Kerr ◽

Duncan Sproul ◽

Ramon Grima

Keyword(s):

Dna Methylation ◽

Large Scale ◽

Field Model ◽

Mean Field ◽

Statistical Properties ◽

Stochastic Simulations ◽

Model Parameters ◽

Mean Field Model ◽

Mean Field Models ◽

Methylation Patterns

The accurate establishment and maintenance of DNA methylation patterns is vital for mammalian development and disruption to these processes causes human disease. Our understanding of DNA methylation mechanisms has been facilitated by mathematical modelling, particularly stochastic simulations. Mega-base scale variation in DNA methylation patterns is observed in development, cancer and ageing and the mechanisms generating these patterns are little understood. However, the computational cost of stochastic simulations prevents them from modelling such large genomic regions. Here we test the utility of three different mean-field models to predict large-scale DNA methylation patterns. By comparison to stochastic simulations, we show that a cluster mean-field model accurately predicts the statistical properties of steady-state DNA methylation patterns, including the mean and variance of methylation levels calculated across a system of CpG sites, as well as the covariance and correlation of methylation levels between neighbouring sites. We also demonstrate that a cluster mean-field model can be used within an approximate Bayesian computation framework to accurately infer model parameters from data. As mean-field models can be solved numerically in a few seconds, our work demonstrates their utility for understanding the processes underpinning large-scale DNA methylation patterns.

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

10.1101/352393 ◽

2018 ◽

Cited By ~ 1

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.

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

Neural Plasticity ◽

10.1155/2021/6623926 ◽

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.

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Optimal responsiveness and information flow in networks of heterogeneous neurons

Scientific Reports ◽

10.1038/s41598-021-96745-2 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Matteo Di Volo ◽

Alain Destexhe

Keyword(s):

Information Flow ◽

Heterogeneous Networks ◽

Large Scale ◽

Computational Models ◽

Field Model ◽

Mean Field ◽

Network Models ◽

Inhibitory Neurons ◽

Mean Field Model ◽

Optimal Responsiveness

AbstractCerebral cortex is characterized by a strong neuron-to-neuron heterogeneity, but it is unclear what consequences this may have for cortical computations, while most computational models consider networks of identical units. Here, we study network models of spiking neurons endowed with heterogeneity, that we treat independently for excitatory and inhibitory neurons. We find that heterogeneous networks are generally more responsive, with an optimal responsiveness occurring for levels of heterogeneity found experimentally in different published datasets, for both excitatory and inhibitory neurons. To investigate the underlying mechanisms, we introduce a mean-field model of heterogeneous networks. This mean-field model captures optimal responsiveness and suggests that it is related to the stability of the spontaneous asynchronous state. The mean-field model also predicts that new dynamical states can emerge from heterogeneity, a prediction which is confirmed by network simulations. Finally we show that heterogeneous networks maximise the information flow in large-scale networks, through recurrent connections. We conclude that neuronal heterogeneity confers different responsiveness to neural networks, which should be taken into account to investigate their information processing capabilities.

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

Neural Computation ◽

10.1162/neco_a_01173 ◽

2019 ◽

Vol 31 (4) ◽

pp. 653-680 ◽

Cited By ~ 13

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.

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Magnetic helicity fluxes in αΩ dynamos

Proceedings of the International Astronomical Union ◽

10.1017/s1743921311007502 ◽

2010 ◽

Vol 6 (S274) ◽

pp. 464-466

Author(s):

Simon Candelaresi ◽

Axel Brandenburg

Keyword(s):

Magnetic Fields ◽

Large Scale ◽

Field Model ◽

Mean Field ◽

Reynolds Numbers ◽

Magnetic Helicity ◽

Small Scale ◽

Mean Field Model ◽

One Dimensional

AbstractIn turbulent dynamos the production of large-scale magnetic fields is accompanied by a separation of magnetic helicity in scale. The large- and small-scale parts increase in magnitude. The small-scale part can eventually work against the dynamo and quench it, especially at high magnetic Reynolds numbers. A one-dimensional mean-field model of a dynamo is presented where diffusive magnetic helicity fluxes within the domain are important. It turns out that this effect helps to alleviate the quenching. Here we show that internal magnetic helicity fluxes, even within one hemisphere, can be important for alleviating catastrophic quenching.

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