1,068 research outputs found
One-Dimensional Population Density Approaches to Recurrently Coupled Networks of Neurons with Noise
Mean-field systems have been previously derived for networks of coupled,
two-dimensional, integrate-and-fire neurons such as the Izhikevich, adapting
exponential (AdEx) and quartic integrate and fire (QIF), among others.
Unfortunately, the mean-field systems have a degree of frequency error and the
networks analyzed often do not include noise when there is adaptation. Here, we
derive a one-dimensional partial differential equation (PDE) approximation for
the marginal voltage density under a first order moment closure for coupled
networks of integrate-and-fire neurons with white noise inputs. The PDE has
substantially less frequency error than the mean-field system, and provides a
great deal more information, at the cost of analytical tractability. The
convergence properties of the mean-field system in the low noise limit are
elucidated. A novel method for the analysis of the stability of the
asynchronous tonic firing solution is also presented and implemented. Unlike
previous attempts at stability analysis with these network types, information
about the marginal densities of the adaptation variables is used. This method
can in principle be applied to other systems with nonlinear partial
differential equations.Comment: 26 Pages, 6 Figure
Synchronization of electrically coupled resonate-and-fire neurons
Electrical coupling between neurons is broadly present across brain areas and
is typically assumed to synchronize network activity. However, intrinsic
properties of the coupled cells can complicate this simple picture. Many cell
types with strong electrical coupling have been shown to exhibit resonant
properties, and the subthreshold fluctuations arising from resonance are
transmitted through electrical synapses in addition to action potentials. Using
the theory of weakly coupled oscillators, we explore the effect of both
subthreshold and spike-mediated coupling on synchrony in small networks of
electrically coupled resonate-and-fire neurons, a hybrid neuron model with
linear subthreshold dynamics and discrete post-spike reset. We calculate the
phase response curve using an extension of the adjoint method that accounts for
the discontinuity in the dynamics. We find that both spikes and resonant
subthreshold fluctuations can jointly promote synchronization. The subthreshold
contribution is strongest when the voltage exhibits a significant post-spike
elevation in voltage, or plateau. Additionally, we show that the geometry of
trajectories approaching the spiking threshold causes a "reset-induced shear"
effect that can oppose synchrony in the presence of network asymmetry, despite
having no effect on the phase-locking of symmetrically coupled pairs
Noise-induced behaviors in neural mean field dynamics
The collective behavior of cortical neurons is strongly affected by the
presence of noise at the level of individual cells. In order to study these
phenomena in large-scale assemblies of neurons, we consider networks of
firing-rate neurons with linear intrinsic dynamics and nonlinear coupling,
belonging to a few types of cell populations and receiving noisy currents.
Asymptotic equations as the number of neurons tends to infinity (mean field
equations) are rigorously derived based on a probabilistic approach. These
equations are implicit on the probability distribution of the solutions which
generally makes their direct analysis difficult. However, in our case, the
solutions are Gaussian, and their moments satisfy a closed system of nonlinear
ordinary differential equations (ODEs), which are much easier to study than the
original stochastic network equations, and the statistics of the empirical
process uniformly converge towards the solutions of these ODEs. Based on this
description, we analytically and numerically study the influence of noise on
the collective behaviors, and compare these asymptotic regimes to simulations
of the network. We observe that the mean field equations provide an accurate
description of the solutions of the network equations for network sizes as
small as a few hundreds of neurons. In particular, we observe that the level of
noise in the system qualitatively modifies its collective behavior, producing
for instance synchronized oscillations of the whole network, desynchronization
of oscillating regimes, and stabilization or destabilization of stationary
solutions. These results shed a new light on the role of noise in shaping
collective dynamics of neurons, and gives us clues for understanding similar
phenomena observed in biological networks
Computational study of resting state network dynamics
Lo scopo di questa tesi è quello di mostrare, attraverso una simulazione con il software The Virtual Brain, le più importanti proprietà della dinamica cerebrale durante il resting state, ovvero quando non si è coinvolti in nessun compito preciso e non si è sottoposti a nessuno stimolo particolare. Si comincia con lo spiegare cos’è il resting state attraverso una breve revisione storica della sua scoperta, quindi si passano in rassegna alcuni metodi sperimentali utilizzati nell’analisi dell’attività cerebrale, per poi evidenziare la differenza tra connettività strutturale e funzionale. In seguito, si riassumono brevemente i concetti dei sistemi dinamici, teoria indispensabile per capire un sistema complesso come il cervello. Nel capitolo successivo, attraverso un approccio ‘bottom-up’, si illustrano sotto il profilo biologico le principali strutture del sistema nervoso, dal neurone alla corteccia cerebrale. Tutto ciò viene spiegato anche dal punto di vista dei sistemi dinamici, illustrando il pionieristico modello di Hodgkin-Huxley e poi il concetto di dinamica di popolazione. Dopo questa prima parte preliminare si entra nel dettaglio della simulazione. Prima di tutto si danno maggiori informazioni sul software The Virtual Brain, si definisce il modello di network del resting state utilizzato nella simulazione e si descrive il ‘connettoma’ adoperato. Successivamente vengono mostrati i risultati dell’analisi svolta sui dati ricavati, dai quali si mostra come la criticità e il rumore svolgano un ruolo chiave nell'emergenza di questa attività di fondo del cervello. Questi risultati vengono poi confrontati con le più importanti e recenti ricerche in questo ambito, le quali confermano i risultati del nostro lavoro. Infine, si riportano brevemente le conseguenze che porterebbe in campo medico e clinico una piena comprensione del fenomeno del resting state e la possibilità di virtualizzare l’attività cerebrale
Synchronised firing patterns in a random network of adaptive exponential integrate-and-fire neuron model
Acknowledgements This study was possible by partial financial support from the following Brazilian government agencies: CNPq, CAPES, and FAPESP (2011/19296-1 and 2015/07311-7). We also wish thank Newton Fund and COFAP.Peer reviewedPostprin
Finite-size and correlation-induced effects in Mean-field Dynamics
The brain's activity is characterized by the interaction of a very large
number of neurons that are strongly affected by noise. However, signals often
arise at macroscopic scales integrating the effect of many neurons into a
reliable pattern of activity. In order to study such large neuronal assemblies,
one is often led to derive mean-field limits summarizing the effect of the
interaction of a large number of neurons into an effective signal. Classical
mean-field approaches consider the evolution of a deterministic variable, the
mean activity, thus neglecting the stochastic nature of neural behavior. In
this article, we build upon two recent approaches that include correlations and
higher order moments in mean-field equations, and study how these stochastic
effects influence the solutions of the mean-field equations, both in the limit
of an infinite number of neurons and for large yet finite networks. We
introduce a new model, the infinite model, which arises from both equations by
a rescaling of the variables and, which is invertible for finite-size networks,
and hence, provides equivalent equations to those previously derived models.
The study of this model allows us to understand qualitative behavior of such
large-scale networks. We show that, though the solutions of the deterministic
mean-field equation constitute uncorrelated solutions of the new mean-field
equations, the stability properties of limit cycles are modified by the
presence of correlations, and additional non-trivial behaviors including
periodic orbits appear when there were none in the mean field. The origin of
all these behaviors is then explored in finite-size networks where interesting
mesoscopic scale effects appear. This study leads us to show that the
infinite-size system appears as a singular limit of the network equations, and
for any finite network, the system will differ from the infinite system
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