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Active Mean Fields: Solving the Mean Field Approximation in the Level Set Framework [chapter]

Kilian M. Pohl, Ron Kikinis, William M. Wells
Lecture Notes in Computer Science  
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

N. Safiullin, N. Kleeorin, S. Porshnev, I. Rogachevskii, A. Ruzmaikin
2018 Journal of Plasma Physics  
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]

V. Ros, G. Biroli, C. Cammarota
2020 arXiv   pre-print
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]

Mengkai Feng, Zhonghuai Hou
2021 arXiv   pre-print
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

Vladimir Shaydurov, Viktoria Kornienko
2019 Journal of Siberian Federal University  
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

D Liley, P Cadusch, M Dafilis
2003 Network  
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

D.T.J. Liley, P.J. Cadusch, M.P. Dafilis
2002 Network  
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]

Cristiano Capone, Matteo di Volo, Alberto Romagnoni, Maurizio Mattia, Alain Destexhe
2019 bioRxiv   pre-print
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

Wassim Haddad
2018 Symmetry  
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

Valentina Ros, Giulio Biroli, Chiara Cammarota
2021 SciPost Physics  
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

Fabio Bagagiolo, Dario Bauso, Raffaele Pesenti
2015 Dynamic Games and Applications  
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

Sandro Romani, Daniel J. Amit, Gianluigi Mongillo
2006 Journal of Computational Neuroscience  
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

Thomas Speck, Andreas M. Menzel, Julian Bialké, Hartmut Löwen
2015 Journal of Chemical Physics  
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

Boris B. Vladimirski, Joël Tabak, Michael J. O'Donovan, John Rinzel
2008 Journal of Computational Neuroscience  
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

Xavier Bresson, Tony F. Chan
2007 Proceedings of IEEE international conference on image processing  
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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