Synchrony-induced modes of oscillation of a neural field model

We investigate the modes of oscillation of heterogeneous ring-networks of quadratic integrate-and-fire (QIF) neurons with non-local, space-dependent coupling. Perturbations of the equilibrium state with a particular wave number produce transient standing waves with a specific temporal frequency, analogous to those in a tense string. In the neuronal network, the equilibrium corresponds to a spatially homogeneous, asynchronous state. Perturbations of this state excite the network’s oscillatory modes, which reflect the interplay of episodes of synchronous spiking with the excitatory-inhibitory spatial interactions. In the thermodynamic limit, an exact low-dimensional neural field model (QIF-NFM) describing the macroscopic dynamics of the network is derived. This allows us to obtain formulas for the Turing eigenvalues of the spatially-homogeneous state, and hence to obtain its stability boundary. We find that the frequency of each Turing mode depends on the corresponding Fourier coefficient of the synaptic pattern of connectivity. The decay rate instead, is identical for all oscillation modes as a consequence of the heterogeneity-induced desynchronization of the neurons. Finally, we numerically compute the spectrum of spatially-inhomogeneous solutions branching from the Turing bifurcation, showing that similar oscillatory modes operate in neural bump states, and are maintained away from onset

Patterns of spike synchrony in neural field models

Els models neuronals de camp mig són descripcions fenomenològiques de l'activitat de xarxes de neurones espacialment organitzades. Gràcies a la seva simplicitat, aquests models són unes eines extremadament útils per a l'anàlisi dels patrons espai-temporals que apareixen a les xarxes neuronals, i s'utilitzen àmpliament en neurociència computacional. És ben sabut que els models de camp mig tradicionals no descriuen adequadament la dinàmica de les xarxes de neurones si aquestes actuen de manera síncrona. No obstant això, les simulacions computacionals de xarxes neuronals demostren que, fins i tot en estats d'alta asincronia, fluctuacions ràpides dels inputs comuns que arriben a les neurones poden provocar períodes transitoris en els quals les neurones de la xarxa es comporten de manera síncrona. A més a més, la sincronització també pot ser generada per la mateixa xarxa, donant lloc a oscil·lacions auto-sostingudes. En aquesta tesi investiguem la presència de patrons espai-temporals deguts a la sincronització en xarxes de neurones heterogènies i espacialment distribuïdes. Aquests patrons no s'observen en els models tradicionals de camp mig, i per aquest motiu han estat àmpliament ignorats en la literatura. Per poder investigar la dinàmica induïda per l'activitat sincronitzada de les neurones, fem servir un nou model de camp mig que es deriva exactament d'una població de neurones de tipus quadratic integrate-and-fire. La simplicitat del model ens permet analitzar l'estabilitat de la xarxa en termes del perfil espacial de la connectivitat sinàptica, i obtenir fórmules exactes per les fronteres d'estabilitat que caracteritzen la dinàmica de la xarxa neuronal original. Aquest mateix anàlisi també revela l'existència d'un conjunt de modes d'oscil·lació que es deuen exclusivament a l'activitat sincronitzada de les neurones. Creiem que els resultats presentats en aquesta tesi inspiraran nous avenços teòrics relacionats amb la dinàmica col·lectiva de les xarxes neuronals, contribuïnt així en el desenvolupament de la neurociència computacional.Neural field models are phenomenological descriptions of the activity of spatially organized, recurrently coupled neuronal networks. Due to their mathematical simplicity, such models are extremely useful for the analysis of spatiotemporal phenomena in networks of spiking neurons, and are largely used in computational neuroscience. Nevertheless, it is well known that traditional neural field descriptions fail to describe the collective dynamics of networks of synchronously spiking neurons. Yet, numerical simulations of networks of spiking neurons show that, even in the case of highly asynchronous activity, fast fluctuations in the common external inputs drive transient episodes of spike synchrony. Moreover, synchronization may also be generated by the network itself, resulting in the appearance of robust large-scale, self-sustained oscillations. In this thesis, we investigate the emergence of synchrony-induced spatiotemporal patterns in spatially distributed networks of heterogeneous spiking neurons. These patterns are not observed in traditional neural field theories and have been largely overlooked in the literature. To investigate synchrony-induced phenomena in neuronal networks, we use a novel neural field model which is exactly derived from a large population of quadratic integrate-and-fire model neurons. The simplicity of the neural field model allows us to analyze the stability of the network in terms of the spatial profile of the synaptic connectivity, and to obtain exact formulas for the stability boundaries characterizing the dynamics of the original spiking neuronal network. Remarkably, the analysis also reveals the existence of a collection of oscillation modes, which are exclusively due to spike-synchronization. We believe that the results presented in this thesis will foster theoretical advances on the collective dynamics of neuronal networks, upgrading the mathematical basis of computational neuroscience

Patterns of spike synchrony in neural field models

Els models neuronals de camp mig són descripcions fenomenològiques de l'activitat de xarxes de neurones espacialment organitzades. Gràcies a la seva simplicitat, aquests models són unes eines extremadament útils per a l'anàlisi dels patrons espai-temporals que apareixen a les xarxes neuronals, i s'utilitzen àmpliament en neurociència computacional. És ben sabut que els models de camp mig tradicionals no descriuen adequadament la dinàmica de les xarxes de neurones si aquestes actuen de manera síncrona. No obstant això, les simulacions computacionals de xarxes neuronals demostren que, fins i tot en estats d'alta asincronia, fluctuacions ràpides dels inputs comuns que arriben a les neurones poden provocar períodes transitoris en els quals les neurones de la xarxa es comporten de manera síncrona. A més a més, la sincronització també pot ser generada per la mateixa xarxa, donant lloc a oscil·lacions auto-sostingudes. En aquesta tesi investiguem la presència de patrons espai-temporals deguts a la sincronització en xarxes de neurones heterogènies i espacialment distribuïdes. Aquests patrons no s'observen en els models tradicionals de camp mig, i per aquest motiu han estat àmpliament ignorats en la literatura. Per poder investigar la dinàmica induïda per l'activitat sincronitzada de les neurones, fem servir un nou model de camp mig que es deriva exactament d'una població de neurones de tipus quadratic integrate-and-fire. La simplicitat del model ens permet analitzar l'estabilitat de la xarxa en termes del perfil espacial de la connectivitat sinàptica, i obtenir fórmules exactes per les fronteres d'estabilitat que caracteritzen la dinàmica de la xarxa neuronal original. Aquest mateix anàlisi també revela l'existència d'un conjunt de modes d'oscil·lació que es deuen exclusivament a l'activitat sincronitzada de les neurones. Creiem que els resultats presentats en aquesta tesi inspiraran nous avenços teòrics relacionats amb la dinàmica col·lectiva de les xarxes neuronals, contribuïnt així en el desenvolupament de la neurociència computacional.Neural field models are phenomenological descriptions of the activity of spatially organized, recurrently coupled neuronal networks. Due to their mathematical simplicity, such models are extremely useful for the analysis of spatiotemporal phenomena in networks of spiking neurons, and are largely used in computational neuroscience. Nevertheless, it is well known that traditional neural field descriptions fail to describe the collective dynamics of networks of synchronously spiking neurons. Yet, numerical simulations of networks of spiking neurons show that, even in the case of highly asynchronous activity, fast fluctuations in the common external inputs drive transient episodes of spike synchrony. Moreover, synchronization may also be generated by the network itself, resulting in the appearance of robust large-scale, self-sustained oscillations. In this thesis, we investigate the emergence of synchrony-induced spatiotemporal patterns in spatially distributed networks of heterogeneous spiking neurons. These patterns are not observed in traditional neural field theories and have been largely overlooked in the literature. To investigate synchrony-induced phenomena in neuronal networks, we use a novel neural field model which is exactly derived from a large population of quadratic integrate-and-fire model neurons. The simplicity of the neural field model allows us to analyze the stability of the network in terms of the spatial profile of the synaptic connectivity, and to obtain exact formulas for the stability boundaries characterizing the dynamics of the original spiking neuronal network. Remarkably, the analysis also reveals the existence of a collection of oscillation modes, which are exclusively due to spike-synchronization. We believe that the results presented in this thesis will foster theoretical advances on the collective dynamics of neuronal networks, upgrading the mathematical basis of computational neuroscience

Flexible integration of continuous sensory evidence in perceptual estimation tasks

Accumulating sensory information over time is crucial for making accurate judgments when acting in the face of noisy or ambiguous sensory information. For example, a hunting predator needs to compute the net direction of motion of a large group of prey (e.g., shoals of fish or birds flying in flock). Here, we study the underlying neural mechanisms by developing a neural network model that can average angular sensory input near-optimally and also signal the reliability of the estimated average direction. Moreover, the network can flexibly give larger weight to either initial or more recent sensory information, as we observe in humans performing an estimation task. Our findings shed light on the neural circuit mechanisms underlying continuous perceptual judgments. Temporal accumulation of evidence is crucial for making accurate judgments based on noisy or ambiguous sensory input. The integration process leading to categorical decisions is thought to rely on competition between neural populations, each encoding a discrete categorical choice. How recurrent neural circuits integrate evidence for continuous perceptual judgments is unknown. Here, we show that a continuous bump attractor network can integrate a circular feature, such as stimulus direction, nearly optimally. As required by optimal integration, the population activity of the network unfolds on a two-dimensional manifold, in which the position of the network's activity bump tracks the stimulus average, and, simultaneously, the bump amplitude tracks stimulus uncertainty. Moreover, the temporal weighting of sensory evidence by the network depends on the relative strength of the stimulus compared to the internally generated bump dynamics, yielding either early (primacy), uniform, or late (recency) weighting. The model can flexibly switch between these regimes by changing a single control parameter, the global excitatory drive. We show that this mechanism can quantitatively explain individual temporal weighting profiles of human observers, and we validate the model prediction that temporal weighting impacts reaction times. Our findings point to continuous attractor dynamics as a plausible neural mechanism underlying stimulus integration in perceptual estimation tasks