scholarly journals Phase-locking patterns underlying effective communication in exact firing rate models of neural networks

2021 ◽  
Author(s):  
David Reyner-Parra ◽  
Gemma Huguet
Keyword(s):  
Phase Locking ◽  
Mean Field ◽  
Effective Communication ◽  
Target Population ◽  
Mean Field Model ◽  
Similar Frequency ◽  
Neuronal Populations ◽  
Spiking Network ◽  
Firing Rate Models ◽  
Low Dimensional

Macroscopic oscillations in the brain have been observed to be involved in many cognitive tasks but their role is not completely understood. One of the suggested functions of the oscillations is to dynamically modulate communication between neural circuits. The Communication Through Coherence (CTC) theory establishes that oscillations reflect rhythmic changes in excitability of the neuronal populations. Thus, populations need to be properly phase-locked so that input volleys arrive at the peaks of excitability of the receiving population to communicate effectively. Here, we present a modeling study to explore synchronization between neuronal circuits connected with unidirectional projections. We consider an Excitatory-Inhibitory (E-I) network of quadratic integrate-and-fire neurons modeling a Pyramidal-Interneuronal Network Gamma (PING) rhythm. The network receives an external periodic input from either one or two sources, simulating the inputs from other oscillating neural groups. We use recently developed mean-field models which provide an exact description of the macroscopic activity of the spiking network. This low-dimensional mean field model allows us to use tools from bifurcation theory to identify the phase-locked states between the input and the target population as a function of the amplitude, frequency and coherence of the inputs. We identify the conditions for optimal phaselocking and selective communication. We find that inputs with high coherence can entrain the network for a wider range of frequencies. Besides, faster oscillatory inputs than the intrinsic network gamma cycle show more effective communication than inputs with similar frequency. Our analysis further shows that the entrainment of the network by inputs with higher frequency is more robust to distractors, thus giving them an advantage to entrain the network. Finally, we show that pulsatile inputs can switch between attended inputs in selective attention.

scholarly journals Chaos in Nonlinear Dynamo Models

1993 ◽  
Vol 157 ◽  
pp. 83-89
Author(s):  
J. Kurths ◽  
A. Brandenburg ◽  
U. Feudel ◽  
W. Jansen
Keyword(s):  
Qualitative Analysis ◽  
Lyapunov Exponents ◽  
Field Model ◽  
Mean Field ◽  
Deterministic Chaos ◽  
Parameter Range ◽  
Hydrodynamic Equations ◽  
Basic Tool ◽  
Mean Field Model ◽  
Low Dimensional

Two nonlinear dynamos have been analyzed by numerical means: 3D-simulation of the magneto-hydrodynamic equations and qualitative analysis of a simplified low-dimensional mean field model. It turns out that both are capable of deterministic chaos in a certain parameter range. As the basic tool the calculation of Lyapunov exponents has been used.

A generalized mean-field model of the natural and high-frequency actuated flow around a high-lift configuration

2009 ◽  
Vol 623 ◽  
pp. 283-316 ◽  
Author(s):  
DIRK M. LUCHTENBURG ◽  
BERT GÜNTHER ◽  
BERND R. NOACK ◽  
RUDIBERT KING ◽  
GILEAD TADMOR
Keyword(s):  
High Frequency ◽  
Field Model ◽  
Mean Field ◽  
Low Frequency ◽  
Navier Stokes ◽  
Mean Field Model ◽  
High Lift ◽  
The Mean ◽  
Generalized Mean ◽  
Low Dimensional

A low-dimensional Galerkin model is proposed for the flow around a high-lift configuration, describing natural vortex shedding, the high-frequency actuated flow with increased lift and transients between both states. The form of the dynamical system has been derived from a generalized mean-field consideration. Steady state and transient URANS (unsteady Reynolds-averaged Navier–Stokes) simulation data are employed to derive the expansion modes and to calibrate the system parameters. The model identifies the mean field as the mediator between the high-frequency actuation and the low-frequency natural shedding instability.

Low dimensional features of the Hamiltonian Mean Field model

2008 ◽  
Author(s):  
Angelo Facchini ◽  
Stefano Ruffo ◽  
Alessandro Campa ◽  
Andrea Giansanti ◽  
Giovanna Morigi ◽  
...  
Keyword(s):  
Field Model ◽  
Mean Field ◽  
Mean Field Model ◽  
Low Dimensional ◽  
Low Dimensional Features

Dynamics of Multiple-Choice Decision Making

2013 ◽  
Vol 25 (8) ◽  
pp. 2108-2145 ◽  
Author(s):  
Hongzhi You ◽  
Da-Hui Wang
Keyword(s):  
Decision Making ◽  
Steady State ◽  
Time Course ◽  
Mean Field ◽  
Decision Time ◽  
Initial State ◽  
Mean Field Model ◽  
Unstable Steady State ◽  
Spiking Network ◽  
Choice Decision

Neuroscientists have carried out comprehensive experiments to reveal the neural mechanisms underlying the perceptual decision making that pervades daily life. These experiments have illuminated salient features of decision making, including probabilistic choice behavior, the ramping activity of decision-related neurons, and the dependence of decision time and accuracy on the difficulty of the task. Spiking network models have reproduced these features, and a two-dimensional mean field model has demonstrated that the saddle node structure underlies two-alternative decision making. Here, we reduced a spiking network model to an analytically tractable, partial integro-differential system and characterized not only multiple-choice decision behaviors but also the time course of neural activities underlying decisions, providing a mechanistic explanation for the observations noted in the experiments. First, we observed that a two-bump unstable steady state of the system is responsible for two-choice decision making, similar to the saddle node structure in the two-dimensional mean field model. However, for four-choice decision making, three types of unstable steady states collectively predominate the time course of the evolution from the initial state to the stable states. Second, the time constant of the unstable steady state can explain the fact that four-choice decision making requires a longer time than two-choice decision making. However, the quicker decision, given a stronger motion strength, cannot be explained by the time constant of the unstable steady state. Rather, the decision time can be attributed to the projection coefficient of the difference between the initial state and the unstable steady state on the eigenvector corresponding to the largest positive eigenvalue.

scholarly journals Coherent oscillations in balanced neural networks driven by endogenous fluctuations

2021 ◽  
Author(s):  
Matteo Di Volo ◽  
Marco Segneri ◽  
Denis Goldobin ◽  
Antonio Politi ◽  
Alessandro Torcini
Keyword(s):  
Mean Field ◽  
Planck Equation ◽  
Structural Heterogeneity ◽  
Mean Field Model ◽  
Self Consistent ◽  
Consistent Solution ◽  
The Mean ◽  
Collective Oscillations ◽  
Low Dimensional ◽  
Parameter Values

We present a detailed analysis of the dynamical regimes observed in a balanced network of identical Quadratic Integrate-and-Fire (QIF) neurons with a sparse connectivity for homogeneous and heterogeneous in-degree distribution. Depending on the parameter values, either an asynchronous regime or periodic oscillations spontaneously emerge. Numerical simulations are compared with a mean field model based on a self-consistent Fokker-Planck equation (FPE). The FPE reproduces quite well the asynchronous dynamics in the homogeneous case by either assuming a Poissonian or renewal distribution for the incoming spike trains. An exact self consistent solution for the mean firing rate obtained in the limit of infinite in-degree allows identifying balanced regimes that can be either mean- or fluctuation-driven. A low-dimensional reduction of the FPE in terms of circular cumulants is also considered. Two cumulants suffice to reproduce the transition scenario observed in the network. The emergence of periodic collective oscillations is well captured both in the homogeneous and heterogeneous setups by the mean field models upon tuning either the connectivity, or the input DC current. In the heterogeneous situation we analyze also the role of structural heterogeneity.

scholarly journals Revisiting a low-dimensional model with short range interactions and mean field critical behavior

2021 ◽  
Author(s):  
Peter Grassberger
Keyword(s):  
Critical Exponents ◽  
Field Model ◽  
Mean Field ◽  
Dimensional Model ◽  
Mean Field Model ◽  
Small Deviations ◽  
Dimensional Version ◽  
Low Dimensional ◽  
2D And 3D ◽  
Non Equilibrium

Abstract In all local low-dimensional models, scaling at critical points deviates from mean field behavior – with one possible exception. This exceptional model with “ordinary” behavior is an inherently non-equilibrium model studied some time ago by H.-M. Bröker and myself. In simulations, its 2-dimensional version suggested that two critical exponents were mean-field, while a third one showed very small deviations. Moreover, the numerics agreed almost perfectly with an explicit mean field model. In the present paper we present simulations with much higher statistics, both for 2d and 3d. In both cases we find that the deviations of all critical exponents from their mean field values are non-leading corrections, and that the scaling is precisely of mean field type. As in the original paper, we propose that the mechanism for this is “confusion”, a strong randomization of the phases of feed-backs that can occur in non-equilibrium systems.

DYNAMICS OF A LARGE ARRAY OF GLOBALLY COUPLED LASERS WITH DISTRIBUTED FREQUENCIES

2001 ◽  
Vol 11 (09) ◽  
pp. 2359-2374 ◽  
Author(s):  
RICARDO A. OLIVA ◽  
STEVEN H. STROGATZ
Keyword(s):  
Field Model ◽  
Natural Frequencies ◽  
Phase Locking ◽  
Mean Field ◽  
Large Array ◽  
Solid State Lasers ◽  
Mean Field Model ◽  
Coupled Nonlinear Oscillators ◽  
Coupled Lasers ◽  
The Stability

We analyze a mean-field model for a large array of coupled solid-state lasers with randomly distributed natural frequencies. Using techniques developed previously for coupled nonlinear oscillators, we derive exact formulas for the stability boundaries of the phase locked, incoherent, and off states, as functions of the coupling and pump strength and the spread of natural frequencies. For parameters in the intermediate regime between total incoherence and perfect phase locking, numerical simulations reveal a variety of unsteady collective states in which all the lasers' intensities vary periodically, quasiperiodically, or chaotically.

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.

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