Collective phenomena in networks of spiking neurons with synaptic delays

A prominent feature of the dynamics of large neuronal networks are the synchrony- driven collective oscillations generated by the interplay between synaptic coupling and synaptic delays. This thesis investigates the emergence of delay-induced oscillations in networks of heterogeneous spiking neurons. Building on recent theoretical advances in exact mean field reductions for neuronal networks, this work explores the dynamics and bifurcations of an exact firing rate model with various forms of synaptic delays. In parallel, the results obtained using the novel firing rate model are compared with extensive numerical simulations of large networks of spiking neurons, which confirm the existence of numerous synchrony-based oscillatory states. Some of these states are novel and display complex forms of partial synchronization and collective chaos. Given the well-known limitation of traditional firing rate models to describe synchrony-based oscillations, previous studies greatly overlooked many of the oscillatory states found here. Therefore, this thesis provides a unique exploration of the oscillatory scenarios found in neuronal networks due to the presence of delays, and may substantially extend the mathematical tools available for modeling the plethora of oscillations detected in electrical recordings of brain activity

Exact firing rate model reveals the differential effects of chemical versus electrical synapses in spiking networks

Chemical and electrical synapses shape the dynamics of neuronal networks. Numerous theoretical studies have investigated how each of these types of synapses contributes to the generation of neuronal oscillations, but their combined effect is less understood. This limitation is further magnified by the impossibility of traditional neuronal mean-field models—also known as firing rate models or firing rate equations—to account for electrical synapses. Here, we introduce a firing rate model that exactly describes the mean-field dynamics of heterogeneous populations of quadratic integrate-and-fire (QIF) neurons with both chemical and electrical synapses. The mathematical analysis of the firing rate model reveals a well-established bifurcation scenario for networks with chemical synapses, characterized by a codimension-2 cusp point and persistent states for strong recurrent excitatory coupling. The inclusion of electrical coupling generally implies neuronal synchrony by virtue of a supercritical Hopf bifurcation. This transforms the cusp scenario into a bifurcation scenario characterized by three codimension-2 points (cusp, Takens-Bogdanov, and saddle-node separatrix loop), which greatly reduces the possibility for persistent states. This is generic for heterogeneous QIF networks with both chemical and electrical couplings. Our results agree with several numerical studies on the dynamics of large networks of heterogeneous spiking neurons with electrical and chemical couplings

26th Annual Computational Neuroscience Meeting (CNS*2017): Part 3 - Meeting Abstracts - Antwerp, Belgium. 15–20 July 2017

This work was produced as part of the activities of FAPESP Research,\ud Disseminations and Innovation Center for Neuromathematics (grant\ud 2013/07699-0, S. Paulo Research Foundation). NLK is supported by a\ud FAPESP postdoctoral fellowship (grant 2016/03855-5). ACR is partially\ud supported by a CNPq fellowship (grant 306251/2014-0)

Dynamics of a large system of spiking neurons with synaptic delay

We analyze a large system of heterogeneous quadratic integrate-and-fire (QIF) neurons with time delayed, all-to-all synaptic coupling. The model is exactly reduced to a system of firing rate equations that is exploited to investigate the existence, stability, and bifurcations of fully synchronous, partially synchronous, and incoherent states. In conjunction with this analysis we perform extensive numerical simulations of the original network of QIF neurons, and determine the relation between the macroscopic and microscopic states for partially synchronous states. The results are summarized in two phase diagrams, for homogeneous and heterogeneous populations, which are obtained analytically to a large extent. For excitatory coupling, the phase diagram is remarkably similar to that of the Kuramoto model with time delays, although here the stability boundaries extend to regions in parameter space where the neurons are not self-sustained oscillators. In contrast, the structure of the boundaries for inhibitory coupling is different, and already for homogeneous networks unveils the presence of various partially synchronized states not present in the Kuramoto model: Collective chaos, quasiperiodic partial synchronization (QPS), and a novel state which we call modulated-QPS (M-QPS). In the presence of heterogeneity partially synchronized states reminiscent to collective chaos, QPS and M-QPS persist. In addition, the presence of heterogeneity greatly amplifies the differences between the incoherence stability boundaries of excitation and inhibition. Finally, we compare our results with those of a traditional (Wilson Cowan-type) firing rate model with time delays. The oscillatory instabilities of the traditional firing rate model qualitatively agree with our results only for the case of inhibitory coupling with strong heterogeneity.We acknowledge support by the Spanish Ministry of Economy and Competitiveness under Projects No. FIS2016-74957-P, No. PSI2016-75688-P, and No. PCIN-2015-127. We also acknowledge support by the European Union’s Horizon 2020 Research and Innovation programme under the Marie Skłodowska-Curie Grant No. 642563

Círculo Malba : sistemas de producción editorial pensados de principio a fin

Fil: Geraci, Máximo Carlos. Universidad de San Andrés. Departamento de Humanidades; Argentina.En el presente trabajo se analizará los desafíos que enfrenta la industria editorial y las diferentes estrategías que el Museo de Arte Latinoamericano de Buenos Aires puede usar para remarcar su posición como referente cultural dentro del ámbito latinoamericano. En primera instancia se llevará a cabo la etapa de investigación donde explicaremos el punto de partida del trabajo y luego los diferentes ejes que marcaron la etapa de descubrimiento. Luego se introducirá la oportunidad y las áreas de acción para empezar a pensar en posibles soluciones. Seguidamente se presentará la propuesta de Círculo Malba, un Sistema Solución que busca posicionar al museo como un generador de contenido, en donde sus usuarios tienen roles tanto activos como pasivos durante la creación de contenido. Por último, se hará un resumen del proceso transcurrido a lo largo del trabajo

The f-I curve Φ(<i>I</i>), Eq (5), for several values of the heterogeneity parameter Δ.

<p>The membrane time constant is <i>τ</i>_<i>m</i> = 10ms.</p

Amplitude of the oscillations of the mean membrane potential for a population of <i>N</i> = 1000 WB neurons.

<p>From left to right: , 0.05 and 0.06. Central and Right panels have <i>σ</i> = 0.01 <i>μ</i>A/cm². See <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005881#sec012" target="_blank">Materials and methods</a> for details.</p

The reduction of the QIF-FRE to Eq (10) breaks down when neurons receive time-varying inputs.

<p>Panels (a-c): <i>S</i>-variable time series for QIF-FRE (solid Black), H-FRE (dashed Black) and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005881#pcbi.1005881.e020" target="_blank">Eq (10)</a> (Blue), for decreasing values of the period <i>T</i>_Θ of the external periodic forcing Θ(<i>t</i>) = 4 + [1 + sin(2<i>πt</i>/<i>T</i>_<i>θ</i>)]³ —shown in panels (g-i). In all cases, the synaptic time constant is slow <i>τ</i>_<i>d</i> = 100 ms, compared to the membrane time constant <i>τ</i>_<i>m</i> = 10 ms. Panels (d-f): <i>R</i>-variable time series. In the case of model <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005881#pcbi.1005881.e020" target="_blank">Eq (10)</a>, the firing rate has been evaluated using <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005881#pcbi.1005881.e019" target="_blank">Eq (9)</a>. Other parameters are <i>J</i> = 21, Δ = 0.3.</p

Networks of heterogeneous inhibitory neurons with fast synaptic kinetics (<i>τ</i>_<i>d</i> = 5 ms) display macroscopic oscillations in the gamma range (ING oscillations) due to collective synchronization.

<p>Panels (a) and (c) show the time series of the synaptic variable <i>S</i> (red) and mean firing rate <i>R</i> (blue), and the raster plot of a population of <i>N</i> = 1000 inhibitory Wang-Buzsáki neurons [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005881#pcbi.1005881.ref030" target="_blank">30</a>] with first order fast synaptic kinetics. The oscillations are suppressed considering slow inhibitory synapses (<i>τ</i>_<i>d</i> = 50 ms), as shown in Panels (b) and (d). See <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005881#sec012" target="_blank">Materials and methods</a> for details on the numerical simulations.</p

The ratio of the width to the center of the distribution of currents Eq (14), <i>δ</i> = Δ/Θ, determines the presence of fast oscillations in the QIF-FRE.

<p>Oscillations disappear above the critical value given by <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005881#pcbi.1005881.e014" target="_blank">Eq (8)</a>. The panels show the Hopf boundaries of QIF-FRE with first-order synapses, for different values of <i>δ</i>, obtained solving the characteristic <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005881#pcbi.1005881.e009" target="_blank">Eq (6)</a> with Re(λ) = 0, see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005881#sec012" target="_blank">Materials and methods</a>. Shaded regions are regions of oscillations. Symbols in the right panel correspond to the parameters used in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005881#pcbi.1005881.g003" target="_blank">Fig 3</a>.</p