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Active Mean Fields: Solving the Mean Field Approximation in the Level Set Framework
[chapter]
Lecture Notes in Computer Science
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Optimizing the resulting estimator by gradient descent leads to a level set style algorithm where the level set functions are the logarithm-of-odds encoding of the posterior label probabilities in an unconstrained ...
Conventional likelihood models are combined with a curve length prior on boundaries, and an approximate posterior distribution on labels is sought via the Mean Field approach. ...
Acknowledgments: We thank Karl Krissen [22] for his level set implementation in the 3D Slicer (www.slicer.org), which we used as a starting point for our AMF implementation. ...
doi:10.1007/978-3-540-73273-0_3
pmid:17633686
pmcid:PMC3265334
dblp:conf/ipmi/PohlKW07
fatcat:jwrz63jp6vhi3a7b37he72uxce
Nonlinear mean-field dynamo and prediction of solar activity
2018
Journal of Plasma Physics
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We apply a nonlinear mean-field dynamo model which includes a budget equation for the dynamics of Wolf numbers to predict solar activity. ...
This instability redistributes the magnetic flux produced by the mean-field dynamo. ...
latitude distribution of the toroidal magnetic field B φ (ϕ) in different stages of the magnetic field evolution obtained in the framework of the dynamo model described in Sec. 2. ...
doi:10.1017/s0022377818000600
fatcat:fv6agtztjzdbzaaju7vcglxfze
Dynamical Instantons and Activated Processes in Mean-Field Glass Models
[article]
2020
arXiv
pre-print
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We focus on the energy landscape of a simple mean-field model of glasses and analyze activated barrier-crossing by combining the Kac-Rice method for high-dimensional Gaussian landscapes with dynamical ...
We show that the associated dynamical mean-field equations admit two solutions: one corresponds to falling back to the original reference minimum, and the other to reaching a new minimum past the barrier ...
Acknowledgements We acknowledge Stefano Sarao Mannelli and Pierfrancesco Urbani for sharing the original version of the code, available at https://github.com/sphinxteam/spiked_matrix-tensor. ...
arXiv:2006.08399v3
fatcat:sxpohll2cffspmqdhxmwreximq
Effective Dynamics of Tracer in Active Bath: A Mean-field Theory Study
[article]
2021
arXiv
pre-print
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By using a mean-field approximation and extending the linearized Dean equation to nonequilibrium environment, we derive a generalized Langevin equation for the tracer particle, wherein colored noise terms ...
We develop a theoretical framework to study the effective dynamics of a tracer immersed in a nonequilibrium bath consisting of active particles. ...
Although we use this mean-field approximation to simply the time evolution equation of collective density, this equation is still to hard to solve. ...
arXiv:2110.00279v1
fatcat:rbtf6lhhing3jl77slq6jjzbuq
"Mean Field Games" as Mathematical Models for Control and Optimization of Business Activity
2019
Journal of Siberian Federal University
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The article is a review of modern mathematical economic models with the "Mean Field Games" structure. ...
For them, the discretization is applied to obtain systems of nonlinear algebraic equations which are solved by computer in an iterative way to get the best instant benefit for each agent. ...
A brief outline of the Mean Field Game model A standard introduction to the mean field game theory starts with a N-player stochastic differential game in which the dynamics of the state ( ) i X t of i-th ...
doi:10.17516/1997-1370-0418
fatcat:hdzcfpq2enbq7jnanowvksxihu
A spatially continuous mean field theory of electrocortical activity
2003
Network
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A set of nonlinear continuum field equations is presented which describes the dynamics of neural activity in cortex. ...
spike activity and limit cycle, chaotic and noise driven oscillations at the frequency of the mammalian alpha rhythm. ...
activity, in this population, gives rise to the notion of the mean neuron. ...
doi:10.1088/0954-898x/14/2/601
fatcat:j7fl3i3wffeulohrdnf3bznsha
A spatially continuous mean field theory of electrocortical activity
2002
Network
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A set of nonlinear continuum field equations is presented which describes the dynamics of neural activity in cortex. ...
spike activity and limit cycle, chaotic and noise driven oscillations at the frequency of the mammalian alpha rhythm. ...
activity, in this population, gives rise to the notion of the mean neuron. ...
doi:10.1080/net.13.1.67.113
pmid:11878285
fatcat:dlnkq544bzanncxdwgow5j32nu
A state-dependent mean-field formalism to model different activity states in conductance based networks of spiking neurons
[article]
2019
bioRxiv
pre-print
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In this context it is important to understand how population dynamics are generated by the designed parameters of the networks, that is the question addressed by mean field theories. ...
predicts the activity in regimes of alternating states like slow oscillations. ...
Acknowledgements This project has received funding from the European Union's Horizon 2020 Framework Programme for Research and Innovation under the Specific Grant Agreements No. 785907 (Human Brain Project ...
doi:10.1101/565127
fatcat:6n4n2etal5fjxah5tqt3wjxv6q
A Computational Study of a Spatiotemporal Mean Field Model Capturing the Emergence of Alpha and Gamma Rhythmic Activity in the Neocortex
2018
Symmetry
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Specifically, we use the spatiotemporal mean field model for capturing the electrical activity in the neocortex to computationally study the emergence of α - and γ -band rhythmic activity in the brain. ...
In this paper, we analyze the spatiotemporal mean field model developed by Liley et al. in order to advance our understanding of the wide effects of pharmacological agents and anesthetics. ...
Acknowledgments: The author thanks James M. Bailey for several helpful discussions on the anesthetic cascade problem and Farshad Shirani for perfoming the numerical simulations in the paper. ...
doi:10.3390/sym10110568
fatcat:qrze5cxqwbdqpnesr24owop4oy
Dynamical instantons and activated processes in mean-field glass models
2021
SciPost Physics
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We focus on the energy landscape of a simple mean-field model of glasses and analyze activated barrier-crossing by combining the Kac-Rice method for high-dimensional Gaussian landscapes with dynamical ...
We show that the associated dynamical mean-field equations admit two solutions: one corresponds to falling back to the original reference minimum, and the other to reaching a new minimum past the barrier ...
Acknowledgements We acknowledge Stefano Sarao Mannelli and Pierfrancesco Urbani for sharing the original version of the code, available at https://github.com/sphinxteam/spiked_matrix-tensor. ...
doi:10.21468/scipostphys.10.1.002
fatcat:w7mvobq5mvdntakz2ecqgq6k5q
Mean-Field Game Modeling the Bandwagon Effect with Activation Costs
2015
Dynamic Games and Applications
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This paper provides a mean-field game theoretic model of the bandwagon effect in social networks. ...
Second, we establish mean-field equilibrium strategies in the case where the mainstream opinion is constant. Such strategies are shown to have a threshold structure. ...
Within the framework of the Eulerian approach, this paper provides a mean-field game theoretic perspective on the problem. ...
doi:10.1007/s13235-015-0167-x
fatcat:v6p63hwztnh5vf7ni3np3e6wwa
Mean-field analysis of selective persistent activity in presence of short-term synaptic depression
2006
Journal of Computational Neuroscience
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The resulting synaptic structure allows the network to exhibit selective persistent activity for each stimulus in the set. ...
Mean-Field theory is extended to recurrent networks of spiking neurons endowed with short-term depression (STD) of synaptic transmission. ...
N.Brunel for important comments on the ms, and the two anonymous referees for helping us significantly improve the presentation. ...
doi:10.1007/s10827-006-6308-x
pmid:16699842
fatcat:kssfepywyrdqxk5424z7jsg674
Dynamical mean-field theory and weakly non-linear analysis for the phase separation of active Brownian particles
2015
Journal of Chemical Physics
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Here we develop and explore this strategy in more detail and show explicitly how to get to such a large-scale, mean-field description starting from the microscopic dynamics. ...
Recently, we have derived an effective Cahn-Hilliard equation for the phase separation dynamics of active Brownian particles by performing a weakly non-linear analysis of the effective hydrodynamic equations ...
ADIABATIC APPROXIMATION For slowly varying fields, we neglect the temporal derivative as well as the viscosity term in Eq. ...
doi:10.1063/1.4922324
pmid:26071703
fatcat:twnn4vhxqjfvtdyoesick3s4fm
Episodic activity in a heterogeneous excitatory network, from spiking neurons to mean field
2008
Journal of Computational Neuroscience
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Various models exhibit features of episodic behavior by means of recurrent excitation for supporting an episode and slow Action Editor: Nicolas Brunel Electronic supplementary material The online version ...
Many developing neural systems exhibit spontaneous activity (O'Donovan, Curr Opin Neurobiol 9:94-104, 1999; Feller, Neuron 22:653-656, 1999) characterized by episodes of discharge (active phases) when ...
Our mean-field framework extends naturally to other neuronal system contexts and can include more biophysical detail when desired. ...
doi:10.1007/s10827-007-0064-4
pmid:18322788
fatcat:5gm3rpimyrd5hheo6ik2efofdq
Active Contours Based on Chambolle's Mean Curvature Motion
2007
Proceedings of IEEE international conference on image processing
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This paper proposes an algorithm to solve most of existing active contour problems based on the approach of mean curvature motion proposed by Chambolle in [1] and the image denoising model of Rudin, Osher ...
The advantage of this new discretization scheme is to use a time step much larger than in standard explicit schemes, which means that less iterations are needed to converge to the steady state solution ...
NUMERICAL SCHEMES We show in this section how to numerically solve the evolution of the GAC and the region-based active contours in this new framework. ...
doi:10.1109/icip.2007.4378884
dblp:conf/icip/BressonC07
fatcat:lvl4feoawnhy3lubomld7pq4nu
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