scholarly journals Poisson-distributed noise induces cortical γ-activity: explanation of γ-enhancement by anaesthetics ketamine and propofol

2021 ◽  
Author(s):  
Thomas Martin Wahl ◽  
Axel Hutt
Keyword(s):  
Coherent State ◽  
Analytical Study ◽  
Additive Noise ◽  
Resonance Effect ◽  
Mean Field ◽  
Inhibitory Neurons ◽  
Frequency Range ◽  
Noise Levels ◽  
Mean Field Model ◽  
The Impact

Abstract Additive noise is known to affect the stability of nonlinear systems. To understand better the role of additive noise in neural systems, we investigate the impact of additive noise on a random neural network of excitatory and inhibitory neurons. Here we hypothesize that the noise originates from the ascending reticular activating system (ARAS). Coherence resonance in the γ-frequency range emerges for intermediate noise levels while the network exhibits non-coherent activity at low and high noise levels. The analytical study of a corresponding mean-field model system explains the resonance effect by a noise-induced phase transition via a saddle-node bifurcation. An analytical study of the linear mean-field systems response to additive noise reveals that the coherent state exhibits a quasi-cycle in the γ-frequency range whose spectral properties are tuned by the additive noise. To illustrate the importance of the work, we show that the quasi-cycle explains γ-enhancement under impact of the anaesthetics ketamine and propofol as a destabilizing effect of the coherent state.

scholarly journals Complex dynamics of synergistic coinfections on realistically clustered networks

2015 ◽  
Vol 112 (33) ◽  
pp. 10551-10556 ◽  
Author(s):  
Laurent Hébert-Dufresne ◽  
Benjamin M. Althouse
Keyword(s):  
Contact Structure ◽  
Complex Dynamics ◽  
Mean Field ◽  
Epidemiological Data ◽  
Single Individual ◽  
Mean Field Model ◽  
Speed Up ◽  
First Order Transition ◽  
Clustered Networks ◽  
The Impact

We investigate the impact of contact structure clustering on the dynamics of multiple diseases interacting through coinfection of a single individual, two problems typically studied independently. We highlight how clustering, which is well known to hinder propagation of diseases, can actually speed up epidemic propagation in the context of synergistic coinfections if the strength of the coupling matches that of the clustering. We also show that such dynamics lead to a first-order transition in endemic states, where small changes in transmissibility of the diseases can lead to explosive outbreaks and regions where these explosive outbreaks can only happen on clustered networks. We develop a mean-field model of coinfection of two diseases following susceptible-infectious-susceptible dynamics, which is allowed to interact on a general class of modular networks. We also introduce a criterion based on tertiary infections that yields precise analytical estimates of when clustering will lead to faster propagation than nonclustered networks. Our results carry importance for epidemiology, mathematical modeling, and the propagation of interacting phenomena in general. We make a call for more detailed epidemiological data of interacting coinfections.

scholarly journals Biologically realistic mean-field models of conductancebased networks of spiking neurons with adaptation

2018 ◽  
Author(s):  
Matteo di Volo ◽  
Alberto Romagnoni ◽  
Cristiano Capone ◽  
Alain Destexhe
Keyword(s):  
Large Scale ◽  
Field Model ◽  
Mean Field ◽  
Inhibitory Neurons ◽  
Activity Levels ◽  
Mean Field Model ◽  
Nonlinear Properties ◽  
Mean Field Models ◽  
The Mean

AbstractAccurate population models are needed to build very large scale neural models, but their derivation is difficult for realistic networks of neurons, in particular when nonlinear properties are involved such as conductance-based interactions and spike-frequency adaptation. Here, we consider such models based on networks of Adaptive exponential Integrate and fire excitatory and inhibitory neurons. Using a Master Equation formalism, we derive a mean-field model of such networks and compare it to the full network dynamics. The mean-field model is capable to correctly predict the average spontaneous activity levels in asynchronous irregular regimes similar to in vivo activity. It also captures the transient temporal response of the network to complex external inputs. Finally, the mean-field model is also able to quantitatively describe regimes where high and low activity states alternate (UP-DOWN state dynamics), leading to slow oscillations. We conclude that such mean-field models are “biologically realistic” in the sense that they can capture both spontaneous and evoked activity, and they naturally appear as candidates to build very large scale models involving multiple brain areas.

scholarly journals A mean-field approach to the dynamics of networks of complex neurons, from nonlinear Integrate-and-Fire to Hodgkin-Huxley models

2019 ◽  
Author(s):  
M. Carlu ◽  
O. Chehab ◽  
L. Dalla Porta ◽  
D. Depannemaecker ◽  
C. Héricé ◽  
...  
Keyword(s):  
Temporal Dynamics ◽  
Mean Field ◽  
Population Models ◽  
Inhibitory Neurons ◽  
Mathematical Tool ◽  
Mean Field Model ◽  
Integrate And Fire ◽  
Mean Field Models ◽  
Electrophysiological Recordings ◽  
Field Formalism

AbstractWe present a mean-field formalism able to predict the collective dynamics of large networks of conductance-based interacting spiking neurons. We apply this formalism to several neuronal models, from the simplest Adaptive Exponential Integrate-and-Fire model to the more complex Hodgkin-Huxley and Morris-Lecar models. We show that the resulting mean-field models are capable of predicting the correct spontaneous activity of both excitatory and inhibitory neurons in asynchronous irregular regimes, typical of cortical dynamics. Moreover, it is possible to quantitatively predict the populations response to external stimuli in the form of external spike trains. This mean-field formalism therefore provides a paradigm to bridge the scale between population dynamics and the microscopic complexity of the individual cells physiology.NEW & NOTEWORTHYPopulation models are a powerful mathematical tool to study the dynamics of neuronal networks and to simulate the brain at macroscopic scales. We present a mean-field model capable of quantitatively predicting the temporal dynamics of a network of complex spiking neuronal models, from Integrate-and-Fire to Hodgkin-Huxley, thus linking population models to neurons electrophysiology. This opens a perspective on generating biologically realistic mean-field models from electrophysiological recordings.

scholarly journals The impact of communications channel bandwidth on the accuracy of pulse-width signal transmission

2021 ◽  
Vol 2094 (3) ◽  
pp. 032021
Author(s):  
V Prokofiev ◽  
O A Golyshevsky ◽  
A E Savochkin
Keyword(s):  
Pulse Width ◽  
Additive Noise ◽  
Pulse Width Modulation ◽  
Signal Transmission ◽  
Pulse Signal ◽  
Frequency Range ◽  
Channel Bandwidth ◽  
Fluctuation Noise ◽  
Harmonic Components ◽  
The Impact

Abstract Pulse-width modulation (PWM) signals used in various areas are sent to the receiver through a communications channel that distorts their waveform due to the limitations of the frequency range. It is not always possible to reduce additive (fluctuation) noises that are also present within the PWM signal to negligible levels. Limiting the range of frequencies transmitted over a communications channel results in both the deterioration of PWM signal front slopes and the changes in the spectral specifications of the fluctuation noise. The simulation of pulse signal formation helped identify a correlation between the pulse front slope and the number of harmonic components transmitted over the communications channel. Through the analysis, we established a correlation between pulse time and the additive noise parameters along with the bandwidth of the real communications channel. These calculations might be useful for problems where it is necessary to formulate the requirements for the communications channel transmitting the PWM signal.

scholarly journals Optimal responsiveness and information flow in networks of heterogeneous neurons

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Matteo Di Volo ◽  
Alain Destexhe
Keyword(s):  
Information Flow ◽  
Heterogeneous Networks ◽  
Large Scale ◽  
Computational Models ◽  
Field Model ◽  
Mean Field ◽  
Network Models ◽  
Inhibitory Neurons ◽  
Mean Field Model ◽  
Optimal Responsiveness

AbstractCerebral cortex is characterized by a strong neuron-to-neuron heterogeneity, but it is unclear what consequences this may have for cortical computations, while most computational models consider networks of identical units. Here, we study network models of spiking neurons endowed with heterogeneity, that we treat independently for excitatory and inhibitory neurons. We find that heterogeneous networks are generally more responsive, with an optimal responsiveness occurring for levels of heterogeneity found experimentally in different published datasets, for both excitatory and inhibitory neurons. To investigate the underlying mechanisms, we introduce a mean-field model of heterogeneous networks. This mean-field model captures optimal responsiveness and suggests that it is related to the stability of the spontaneous asynchronous state. The mean-field model also predicts that new dynamical states can emerge from heterogeneity, a prediction which is confirmed by network simulations. Finally we show that heterogeneous networks maximise the information flow in large-scale networks, through recurrent connections. We conclude that neuronal heterogeneity confers different responsiveness to neural networks, which should be taken into account to investigate their information processing capabilities.

scholarly journals Hyperons and quarks in proto-neutron stars

2019 ◽  
Vol 486 (4) ◽  
pp. 5441-5447 ◽  
Author(s):  
J Roark ◽  
X Du ◽  
C Constantinou ◽  
V Dexheimer ◽  
A W Steiner ◽  
...  
Keyword(s):  
Neutron Stars ◽  
Finite Temperature ◽  
Degrees Of Freedom ◽  
Mean Field ◽  
Large Mass ◽  
Stellar Structure ◽  
Stellar Rotation ◽  
Mean Field Model ◽  
Relativistic Mean Field ◽  
The Impact

ABSTRACT In this work, we study matter in the cores of proto-neutron stars, focusing on the impact of their composition on the stellar structure. We begin by examining the effects of finite temperature (through a fixed entropy per baryon) and lepton fraction on purely nucleonic matter by making use of the DSH (Du, Steiner & Holt) model. We then turn our attention to a relativistic mean-field model containing exotic degrees of freedom, the Chiral Mean Field (CMF) model, again, under the conditions of finite temperature and trapped neutrinos. In the latter, since both hyperons and quarks are found in the cores of large-mass stars, their interplay and the possibility of mixtures of phases is taken into account and analysed. Finally, we discuss how stellar rotation can affect our results.

scholarly journals Modelling digital and manual contact tracing for COVID-19. Are low uptakes and missed contacts deal-breakers?

PLoS ONE ◽  
2021 ◽  
Vol 16 (11) ◽  
pp. e0259969
Author(s):  
Andrei C. Rusu ◽  
Rémi Emonet ◽  
Katayoun Farrahi
Keyword(s):  
Field Model ◽  
Mean Field ◽  
Health Interventions ◽  
Contact Tracing ◽  
Public Health Interventions ◽  
Mean Field Model ◽  
Pathogen Dynamics ◽  
Usage Patterns ◽  
The Right ◽  
The Impact

Comprehensive testing schemes, followed by adequate contact tracing and isolation, represent the best public health interventions we can employ to reduce the impact of an ongoing epidemic when no or limited vaccine supplies are available and the implications of a full lockdown are to be avoided. However, the process of tracing can prove feckless for highly-contagious viruses such as SARS-CoV-2. The interview-based approaches often miss contacts and involve significant delays, while digital solutions can suffer from insufficient adoption rates or inadequate usage patterns. Here we present a novel way of modelling different contact tracing strategies, using a generalized multi-site mean-field model, which can naturally assess the impact of manual and digital approaches alike. Our methodology can readily be applied to any compartmental formulation, thus enabling the study of more complex pathogen dynamics. We use this technique to simulate a newly-defined epidemiological model, SEIR-T, and show that, given the right conditions, tracing in a COVID-19 epidemic can be effective even when digital uptakes are sub-optimal or interviewers miss a fair proportion of the contacts.

scholarly journals Hamiltonian mean-field model: effect of temporal perturbation in coupling matrix

2018 ◽  
Vol 32 (14) ◽  
pp. 1850147 ◽  
Author(s):  
Nivedita Bhadra ◽  
Soumen K. Patra
Keyword(s):  
Critical Point ◽  
Numerical Study ◽  
Coupling Parameter ◽  
Modulation Frequency ◽  
Mean Field ◽  
Critical Energy ◽  
Temporal Modulation ◽  
Coupling Matrix ◽  
Mean Field Model ◽  
The Impact

The Hamiltonian mean-field (HMF) model is a system of fully coupled rotators which exhibits a second-order phase transition at some critical energy in its canonical ensemble. We investigate the case where the interaction between the rotors is governed by a time-dependent coupling matrix. Our numerical study reveals a shift in the critical point due to the temporal modulation. The shift in the critical point is shown to be independent of the modulation frequency above some threshold value, whereas the impact of the amplitude of modulation is dominant. In the microcanonical ensemble, the system with constant coupling reaches a quasi-stationary state (QSS) at an energy near the critical point. Our result indicates that the QSS subsists in presence of such temporal modulation of the coupling parameter.

scholarly journals Equations governing dynamics of excitation and inhibition in the mouse corticothalamic network

2020 ◽  
Author(s):  
I-Chun Lin ◽  
Michael Okun ◽  
Matteo Carandini ◽  
Kenneth D. Harris
Keyword(s):  
Cortical Neurons ◽  
Mean Field ◽  
Inhibitory Neurons ◽  
Cortical Circuits ◽  
Mean Field Model ◽  
Population Activity ◽  
Cortical Dynamics ◽  
Mean Field Models ◽  
Cortical Responses ◽  
Mouse Visual Cortex

Although cortical circuits are complex and interconnected with the rest of the brain, their macroscopic dynamics are often approximated by modeling the averaged activities of excitatory and inhibitory cortical neurons, without interactions with other brain circuits. To verify the validity of such mean-field models, we optogenetically stimulated populations of excitatory and parvalbumin-expressing inhibitory neurons in awake mouse visual cortex, while recording population activity in cortex and in its thalamic correspondent, the lateral geniculate nucleus. The cortical responses to brief test pulses could not be explained by a mean-field model including only cortical excitatory and inhibitory populations. However, these responses could be predicted by extending the model to include thalamic interactions that cause net cortical suppression following activation of cortical excitatory neurons. We conclude that mean-field models can accurately summarize cortical dynamics, but only when the cortex is considered as part of a dynamic corticothalamic network.

scholarly journals Biologically Realistic Mean-Field Models of Conductance-Based Networks of Spiking Neurons with Adaptation

2019 ◽  
Vol 31 (4) ◽  
pp. 653-680 ◽  
Author(s):  
Matteo di Volo ◽  
Alberto Romagnoni ◽  
Cristiano Capone ◽  
Alain Destexhe
Keyword(s):  
Large Scale ◽  
Field Model ◽  
Mean Field ◽  
Inhibitory Neurons ◽  
Activity Levels ◽  
Mean Field Model ◽  
Nonlinear Properties ◽  
Mean Field Models ◽  
The Mean

Accurate population models are needed to build very large-scale neural models, but their derivation is difficult for realistic networks of neurons, in particular when nonlinear properties are involved, such as conductance-based interactions and spike-frequency adaptation. Here, we consider such models based on networks of adaptive exponential integrate-and-fire excitatory and inhibitory neurons. Using a master equation formalism, we derive a mean-field model of such networks and compare it to the full network dynamics. The mean-field model is capable of correctly predicting the average spontaneous activity levels in asynchronous irregular regimes similar to in vivo activity. It also captures the transient temporal response of the network to complex external inputs. Finally, the mean-field model is also able to quantitatively describe regimes where high- and low-activity states alternate (up-down state dynamics), leading to slow oscillations. We conclude that such mean-field models are biologically realistic in the sense that they can capture both spontaneous and evoked activity, and they naturally appear as candidates to build very large-scale models involving multiple brain areas.

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