Patterns of spike synchrony in neural field models
Loading...
Document Type
Document Version
Author
Director
Montbrió, Ernest
Tutor
Other authors
Publication Date
Pages
130 p.
Embargo date
License
Citation
Esnaola Acebes, J. Patterns of spike synchrony in neural field models. Universitat Pompeu Fabra; 2018. handle: http://hdl.handle.net/10803/663871
This citation was generated automatically.
Citation
Doctoral program
Programa de doctorat en Tecnologies de la Informació i les Comunicacions
Abstract
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.
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.
Keywords
Mathematical neuroscience, Spatiotemporal patterns, Oscillations, Bump states, Synchronization, Neural population, Firing rate, Population model, Spiking neurons, Quadratic-integrate-and-fire, Neural-field, Mean-field
Subjects
62 - Engineering. Technology
Publisher
Universitat Pompeu Fabra
