scholarly journals Mean field approximation of network of biophysical neurons driven by conductance-based ion exchange dynamics

2021 ◽  
Author(s):  
Abhirup Bandyopadhyay ◽  
Spase Petkoski ◽  
Viktor Jirsa
Keyword(s):  
Ion Exchange ◽  
Molecular Mechanisms ◽  
Field Model ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Mean Field Model ◽  
Ion Concentrations ◽  
The Mean ◽  
Locally Homogeneous

Changes in extracellular ion concentrations are known to modulate neuronal excitability and play a major role in controlling the neuronal firing rate, not just during the healthy homeostasis, but also in pathological conditions such as epilepsy. The microscopic molecular mechanisms of field effects are understood, but the precise correspondence between the microscopic mechanisms of ion exchange in the cellular space of neurons and the macroscopic behavior of neuronal populations remains to be established. We derive a mean field model of a population of Hodgkin Huxley type neurons. This model links the neuronal intra- and extra-cellular ion concentrations to the mean membrane potential and the mean synaptic input in terms of the synaptic conductance of the locally homogeneous mesoscopic network and can describe various brain activities including multi-stability at resting states, as well as more pathological spiking and bursting behaviors, and depolarizations. The results from the analytical solution of the mean field model agree with the mean behavior of numerical simulations of large-scale networks of neurons. The mean field model is analytically exact for non-autonomous ion concentration variables and provides a mean field approximation in the thermodynamic limit, for locally homogeneous mesoscopic networks of biophysical neurons driven by an ion exchange mechanism. These results may provide the missing link between high-level neural mass approaches which are used in the brain network modeling and physiological parameters that drive the neuronal dynamics.

Dynamical Mean Field Model of a Neural-Glial Mass

2010 ◽  
Vol 22 (4) ◽  
pp. 969-997 ◽  
Author(s):  
Roberto C. Sotero ◽  
Ramón Martínez-Cancino
Keyword(s):  
Differential Equations ◽  
Field Model ◽  
Mean Field ◽  
Field Approximation ◽  
Presynaptic Terminal ◽  
Mean Field Approximation ◽  
Nerve Terminals ◽  
Mean Field Model ◽  
Wide Range ◽  
Activity Dependent

Our goal is to model the behavior of an ensemble of interacting neurons and astrocytes (the neural-glial mass). For this, a model describing N tripartite synapses is proposed. Each tripartite synapse consists of presynaptic and postsynaptic nerve terminals, as well as the synaptically associated astrocytic microdomain, and is described by a system of 13 stochastic differential equations. Then, by applying the dynamical mean field approximation (DMA) (Hasegawa, 2003a , 2003b ) the system of 13N equations is reduced to 13(13 + 2) = 195 deterministic differential equations for the means and the second-order moments of local and global variables. Simulations are carried out for studying the response of the neural-glial mass to external inputs applied to either the presynaptic terminals or the astrocytes. Three cases were considered: the astrocytes influence only the presynaptic terminal, only the postsynaptic terminal, or both the presynaptic and postsynaptic terminals. As a result, a wide range of responses varying from singles spikes to train of spikes was evoked on presynaptic and postsynaptic terminals. The experimentally observed phenomenon of spontaneous activity in astrocytes was replicated on the neural-glial mass. The model predicts that astrocytes can have a strong and activity-dependent influence on synaptic transmission. Finally, simulations show that the dynamics of astrocytes influences the synchronization ratio between neurons, predicting a peak in the synchronization for specific values of the astrocytes’ parameters.

scholarly journals The structure of musical harmony as an ordered phase of sound: A statistical mechanics approach to music theory

2019 ◽  
Vol 5 (5) ◽  
pp. eaav8490 ◽  
Author(s):  
Jesse Berezovsky
Keyword(s):  
Phase Transitions ◽  
Statistical Mechanics ◽  
Music Theory ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Mean Field Model ◽  
Musical Harmony ◽  
Emergent Order ◽  
The Mean

Music, while allowing nearly unlimited creative expression, almost always conforms to a set of rigid rules at a fundamental level. The description and study of these rules, and the ordered structures that arise from them, is the basis of the field of music theory. Here, I present a theoretical formalism that aims to explain why basic ordered patterns emerge in music, using the same statistical mechanics framework that describes emergent order across phase transitions in physical systems. I first apply the mean field approximation to demonstrate that phase transitions occur in this model from disordered sound to discrete sets of pitches, including the 12-fold octave division used in Western music. Beyond the mean field model, I use numerical simulation to uncover emergent structures of musical harmony. These results provide a new lens through which to view the fundamental structures of music and to discover new musical ideas to explore.

scholarly journals Relativistic Mean-Field Approximation with Density-Dependent Screening Meson Masses in Nuclear Matter

2003 ◽  
Vol 12 (04) ◽  
pp. 543-554 ◽  
Author(s):  
Bao-Xi Sun ◽  
Xiao-Fu Lu ◽  
Peng-Nian Shen ◽  
En-Guang Zhao
Keyword(s):  
Nuclear Matter ◽  
Field Model ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Mean Field Model ◽  
Density Dependent ◽  
Relativistic Mean Field ◽  
Saturation Properties ◽  
The Masses

The Debye screening masses of the σ, ω and neutral ρ mesons and the photon are calculated in the relativistic mean-field approximation. As the density of the nucleon increases, all the screening masses of mesons increase. A different result with Brown–Rho scaling is shown, which implies a reduction in the mass of all the mesons in the nuclear matter, except the pion. Replacing the masses of the mesons with their corresponding screening masses in the Walecka-1 model, five saturation properties of the nuclear matter are fixed reasonably, and then a density-dependent relativistic mean-field model is proposed without introducing the nonlinear self-coupling terms of mesons.

scholarly journals The Combined Effect of Rotation and Magnetic Field on Finite-Amplitude Thermal Convection

1973 ◽  
Vol 26 (5) ◽  
pp. 617 ◽  
Author(s):  
R Van der Borght ◽  
JO Murphy
Keyword(s):  
Magnetic Field ◽  
Mean Field ◽  
Field Approximation ◽  
Finite Amplitude ◽  
Combined Effect ◽  
Mean Field Approximation ◽  
Free Boundaries ◽  
Wide Range ◽  
The Mean ◽  
Basic Equations

The combined effect of an imposed rotation and magnetic field on convective transfer in a horizontal Boussinesq layer of fluid heated from below is studied in the mean field approximation. The basic equations are derived by a variational technique and their solutions are then found over a wide range of conditions, in the case of free boundaries, by numerical and analytic techniques, in particular by asymptotic and perturbation methods. The results obtained by the different techniques are shown to be in excellent agreement. As for the linear theory, the calculations predict that the simultaneous presence' of a magnetic field and rotation may produce conflicting tendencies.

scholarly journals Locating the critical end point using the linear sigma model coupled to quarks.

2018 ◽  
Vol 172 ◽  
pp. 02003
Author(s):  
Alejandro Ayala ◽  
J. A. Flores ◽  
L. A. Hernández ◽  
S. Hernández-Ortiz
Keyword(s):  
Sigma Model ◽  
Chemical Potential ◽  
Potential Temperature ◽  
Mean Field ◽  
Field Approximation ◽  
Baryon Density ◽  
Linear Sigma Model ◽  
Mean Field Approximation ◽  
End Point ◽  
The Mean

We use the linear sigma model coupled to quarks to compute the effective potential beyond the mean field approximation, including the contribution of the ring diagrams at finite temperature and baryon density. We determine the model couplings and use them to study the phase diagram in the baryon chemical potential-temperature plane and to locate the Critical End Point.

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