Dual mean field search for large scale linear and quadratic knapsack problems

2017 ◽  
Vol 478 ◽  
pp. 158-167 ◽  
Author(s):  
Juan Banda ◽  
Jonás Velasco ◽  
Arturo Berrones
Keyword(s):  
Large Scale ◽  
Mean Field ◽  
Knapsack Problems ◽  
Quadratic Knapsack

scholarly journals On the Throughput Optimization in Large-Scale Batch-Processing Systems

2021 ◽  
Vol 48 (3) ◽  
pp. 128-129
Author(s):  
Sounak Kar ◽  
Robin Rehrmann ◽  
Arpan Mukhopadhyay ◽  
Bastian Alt ◽  
Florin Ciucu ◽  
...  
Keyword(s):  
Large Scale ◽  
Mean Field ◽  
Queueing Network ◽  
Processing System ◽  
Batch Size ◽  
System Throughput ◽  
Throughput Optimization ◽  
Mean Field Model ◽  
Optimal Batch Size ◽  
Globally Attractive

We analyze a data-processing system with n clients producing jobs which are processed in batches by m parallel servers; the system throughput critically depends on the batch size and a corresponding sub-additive speedup function that arises due to overhead amortization. In practice, throughput optimization relies on numerical searches for the optimal batch size which is computationally cumbersome. In this paper, we model this system in terms of a closed queueing network assuming certain forms of service speedup; a standard Markovian analysis yields the optimal throughput in w n4 time. Our main contribution is a mean-field model that has a unique, globally attractive stationary point, derivable in closed form. This point characterizes the asymptotic throughput as a function of the batch size that can be calculated in O(1) time. Numerical settings from a large commercial system reveal that this asymptotic optimum is accurate in practical finite regimes.

scholarly journals Mean-Field Models for EEG/MEG: From Oscillations to Waves

2021 ◽  
Author(s):  
Áine Byrne ◽  
James Ross ◽  
Rachel Nicks ◽  
Stephen Coombes
Keyword(s):  
Gap Junction ◽  
Large Scale ◽  
Mean Field ◽  
Coarse Grained ◽  
Neural Mass Model ◽  
Neuron Network ◽  
Mass Model ◽  
Mean Field Model ◽  
Neural Mass ◽  
The Rich

AbstractNeural mass models have been used since the 1970s to model the coarse-grained activity of large populations of neurons. They have proven especially fruitful for understanding brain rhythms. However, although motivated by neurobiological considerations they are phenomenological in nature, and cannot hope to recreate some of the rich repertoire of responses seen in real neuronal tissue. Here we consider a simple spiking neuron network model that has recently been shown to admit an exact mean-field description for both synaptic and gap-junction interactions. The mean-field model takes a similar form to a standard neural mass model, with an additional dynamical equation to describe the evolution of within-population synchrony. As well as reviewing the origins of this next generation mass model we discuss its extension to describe an idealised spatially extended planar cortex. To emphasise the usefulness of this model for EEG/MEG modelling we show how it can be used to uncover the role of local gap-junction coupling in shaping large scale synaptic waves.

scholarly journals On the dynamical interaction between overshooting convection and an underlying dipole magnetic field – I. The non-dynamo regime

2021 ◽  
Vol 503 (1) ◽  
pp. 362-375
Author(s):  
L Korre ◽  
NH Brummell ◽  
P Garaud ◽  
C Guervilly
Keyword(s):  
Magnetic Field ◽  
Turbulent Diffusion ◽  
Large Scale ◽  
Molecular Diffusion ◽  
Mean Field ◽  
Stable Region ◽  
Turbulent Regime ◽  
Poloidal Magnetic Field ◽  
Dynamical Interaction ◽  
Large Scale Field

ABSTRACT Motivated by the dynamics in the deep interiors of many stars, we study the interaction between overshooting convection and the large-scale poloidal fields residing in radiative zones. We have run a suite of 3D Boussinesq numerical calculations in a spherical shell that consists of a convection zone with an underlying stable region that initially compactly contains a dipole field. By varying the strength of the convective driving, we find that, in the less turbulent regime, convection acts as turbulent diffusion that removes the field faster than solely molecular diffusion would do. However, in the more turbulent regime, turbulent pumping becomes more efficient and partially counteracts turbulent diffusion, leading to a local accumulation of the field below the overshoot region. These simulations suggest that dipole fields might be confined in underlying stable regions by highly turbulent convective motions at stellar parameters. The confinement is of large-scale field in an average sense and we show that it is reasonably modelled by mean-field ideas. Our findings are particularly interesting for certain models of the Sun, which require a large-scale, poloidal magnetic field to be confined in the solar radiative zone in order to explain simultaneously the uniform rotation of the latter and the thinness of the solar tachocline.

scholarly journals An integral control formulation of mean field game based large scale coordination of loads in smart grids

Automatica ◽  
2019 ◽  
Vol 100 ◽  
pp. 312-322 ◽  
Author(s):  
Arman C. Kizilkale ◽  
Rabih Salhab ◽  
Roland P. Malhamé
Keyword(s):  
Smart Grids ◽  
Large Scale ◽  
Mean Field ◽  
Integral Control ◽  
Mean Field Game

scholarly journals Continuum limit of the vibrational properties of amorphous solids

2017 ◽  
Vol 114 (46) ◽  
pp. E9767-E9774 ◽  
Author(s):  
Hideyuki Mizuno ◽  
Hayato Shiba ◽  
Atsushi Ikeda
Keyword(s):  
Large Scale ◽  
Continuum Limit ◽  
Scaling Law ◽  
Mean Field ◽  
Low Frequency ◽  
Amorphous Solids ◽  
Mode Analysis ◽  
Vibrational Modes ◽  
Phonon Modes ◽  
The Continuum

The low-frequency vibrational and low-temperature thermal properties of amorphous solids are markedly different from those of crystalline solids. This situation is counterintuitive because all solid materials are expected to behave as a homogeneous elastic body in the continuum limit, in which vibrational modes are phonons that follow the Debye law. A number of phenomenological explanations for this situation have been proposed, which assume elastic heterogeneities, soft localized vibrations, and so on. Microscopic mean-field theories have recently been developed to predict the universal non-Debye scaling law. Considering these theoretical arguments, it is absolutely necessary to directly observe the nature of the low-frequency vibrations of amorphous solids and determine the laws that such vibrations obey. Herein, we perform an extremely large-scale vibrational mode analysis of a model amorphous solid. We find that the scaling law predicted by the mean-field theory is violated at low frequency, and in the continuum limit, the vibrational modes converge to a mixture of phonon modes that follow the Debye law and soft localized modes that follow another universal non-Debye scaling law.

scholarly journals Convection and Dynamo in Newly Born Neutron Stars

2022 ◽  
Vol 924 (2) ◽  
pp. 75
Author(s):  
Youhei Masada ◽  
Tomoya Takiwaki ◽  
Kei Kotake
Keyword(s):  
Spherical Shell ◽  
Neutron Stars ◽  
Large Scale ◽  
Convection Zone ◽  
Turbulent Transport ◽  
Mean Field ◽  
Magnetic Component ◽  
Large Scale Structures ◽  
Scale Structures ◽  
Convective Model

Abstract To study properties of magnetohydrodynamic (MHD) convection and resultant dynamo activities in proto-neutron stars (PNSs), we construct a “PNS in a box” simulation model and solve the compressible MHD equation coupled with a nuclear equation of state (EOS) and simplified leptonic transport. As a demonstration, we apply it to two types of PNS model with different internal structures: a fully convective model and a spherical-shell convection model. By varying the spin rate of the models, the rotational dependence of convection and the dynamo that operate inside the PNS is investigated. We find that, as a consequence of turbulent transport by rotating stratified convection, large-scale structures of flow and thermodynamic fields are developed in all models. Depending on the spin rate and the depth of the convection zone, various profiles of the large-scale structures are obtained, which can be physically understood as steady-state solutions to the “mean-field” equation of motion. Additionally to those hydrodynamic structures, a large-scale magnetic component of  ( 10 15 ) G is also spontaneously organized in disordered tangled magnetic fields in all models. The higher the spin rate, the stronger the large-scale magnetic component grows. Intriguingly, as an overall trend, the fully convective models have a stronger large-scale magnetic component than that in the spherical-shell convection models. The deeper the convection zone extends, the larger the size of the convective eddies becomes. As a result, rotationally constrained convection seems to be more easily achieved in the fully convective model, resulting in a higher efficiency of the large-scale dynamo there. To gain a better understanding of the origin of the diversity of a neutron star’s magnetic field, we need to study the PNS dynamo in a wider parameter range.

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