Wilten Nicola

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Recently, a class of two-dimensional integrate and fire models has been used to faithfully model spiking neurons. This class includes the Izhikevich model, the adaptive exponential integrate and fire model, and the quartic integrate and fire model. The bifurcation types for the individual neurons have been thoroughly analyzed by Touboul (SIAM J Appl Math(More)
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(More)
Determining the biological details and mechanisms that are essential for the generation of population rhythms in the mammalian brain is a challenging problem. This problem cannot be addressed either by experimental or computational studies in isolation. Here we show that computational models that are carefully linked with experiment provide insight into(More)
We analytically derive mean-field models for all-to-all coupled networks of heterogeneous, adapting, two-dimensional integrate and fire neurons. The class of models we consider includes the Izhikevich, adaptive exponential, and quartic integrate and fire models. The heterogeneity in the parameters leads to different moment closure assumptions that can be(More)
We analytically derive mean-field models for all-to-all coupled networks of heterogeneous, adapting, two-dimensional integrate and fire neurons. The class of models we consider includes the Izhikevich, adaptive exponential and quartic integrate and fire models. The heterogeneity in the parameters leads to different moment closure assumptions that can be(More)
The hippocampus is a brain structure critical for memory functioning. Its network dynamics include several patterns such as sharp waves that are generated in the CA3 region. To understand how population outputs are generated, models need to consider aspects of network size, cellular and synaptic characteristics and context, which are necessarily ‘balanced’(More)
Mean-field systems have been recently derived that adequately predict the behaviors of large networks of coupled integrate-and-fire neurons [14]. The mean-field system for a network of neurons with spike frequency adaptation is typically a pair of differential equations for the mean adaptation and mean synaptic gating variable of the network. These(More)
Large networks of integrate-and-fire (IF) model neurons are often used to simulate and study the behaviour of biologically realistic networks. However, to fully study the large network behaviour requires an exploration of large regions of a multidimensional parameter space. Such exploration is generally not feasible with large network models, due to the(More)
Cortical oscillations are thought to be involved in many cognitive functions and processes. Several mechanisms have been proposed to regulate oscillations. One prominent but understudied mechanism is gap-junctional coupling. Gap junctions are ubiquitous in cortex between GABAergic interneurons. Moreover, recent experiments indicate their strength can be(More)