Intrinsic adaptation in autonomous recurrent neural networks

A massively recurrent neural network responds on one side to input stimuli and is autonomously active, on the other side, in the absence of sensory inputs. Stimuli and information processing depends crucially on the qualia of the autonomous-state dynamics of the ongoing neural activity. This default neural activity may be dynamically structured in time and space, showing regular, synchronized, bursting or chaotic activity patterns. We study the influence of non-synaptic plasticity on the default dynamical state of recurrent neural networks. The non-synaptic adaption considered acts on intrinsic neural parameters, such as the threshold and the gain, and is driven by the optimization of the information entropy. We observe, in the presence of the intrinsic adaptation processes, three distinct and globally attracting dynamical regimes, a regular synchronized, an overall chaotic and an intermittent bursting regime. The intermittent bursting regime is characterized by intervals of regular flows, which are quite insensitive to external stimuli, interseeded by chaotic bursts which respond sensitively to input signals. We discuss these finding in the context of self-organized information processing and critical brain dynamics.Comment: 24 pages, 8 figure

The geometry of spontaneous spiking in neuronal networks

The mathematical theory of pattern formation in electrically coupled networks of excitable neurons forced by small noise is presented in this work. Using the Freidlin-Wentzell large deviation theory for randomly perturbed dynamical systems and the elements of the algebraic graph theory, we identify and analyze the main regimes in the network dynamics in terms of the key control parameters: excitability, coupling strength, and network topology. The analysis reveals the geometry of spontaneous dynamics in electrically coupled network. Specifically, we show that the location of the minima of a certain continuous function on the surface of the unit n-cube encodes the most likely activity patterns generated by the network. By studying how the minima of this function evolve under the variation of the coupling strength, we describe the principal transformations in the network dynamics. The minimization problem is also used for the quantitative description of the main dynamical regimes and transitions between them. In particular, for the weak and strong coupling regimes, we present asymptotic formulas for the network activity rate as a function of the coupling strength and the degree of the network. The variational analysis is complemented by the stability analysis of the synchronous state in the strong coupling regime. The stability estimates reveal the contribution of the network connectivity and the properties of the cycle subspace associated with the graph of the network to its synchronization properties. This work is motivated by the experimental and modeling studies of the ensemble of neurons in the Locus Coeruleus, a nucleus in the brainstem involved in the regulation of cognitive performance and behavior

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

Dwelling Quietly in the Rich Club: Brain Network Determinants of Slow Cortical Fluctuations

For more than a century, cerebral cartography has been driven by investigations of structural and morphological properties of the brain across spatial scales and the temporal/functional phenomena that emerge from these underlying features. The next era of brain mapping will be driven by studies that consider both of these components of brain organization simultaneously -- elucidating their interactions and dependencies. Using this guiding principle, we explored the origin of slowly fluctuating patterns of synchronization within the topological core of brain regions known as the rich club, implicated in the regulation of mood and introspection. We find that a constellation of densely interconnected regions that constitute the rich club (including the anterior insula, amygdala, and precuneus) play a central role in promoting a stable, dynamical core of spontaneous activity in the primate cortex. The slow time scales are well matched to the regulation of internal visceral states, corresponding to the somatic correlates of mood and anxiety. In contrast, the topology of the surrounding "feeder" cortical regions show unstable, rapidly fluctuating dynamics likely crucial for fast perceptual processes. We discuss these findings in relation to psychiatric disorders and the future of connectomics.Comment: 35 pages, 6 figure

Transition to chaos in random neuronal networks

Firing patterns in the central nervous system often exhibit strong temporal irregularity and heterogeneity in their time averaged response properties. Previous studies suggested that these properties are outcome of an intrinsic chaotic dynamics. Indeed, simplified rate-based large neuronal networks with random synaptic connections are known to exhibit sharp transition from fixed point to chaotic dynamics when the synaptic gain is increased. However, the existence of a similar transition in neuronal circuit models with more realistic architectures and firing dynamics has not been established. In this work we investigate rate based dynamics of neuronal circuits composed of several subpopulations and random connectivity. Nonzero connections are either positive-for excitatory neurons, or negative for inhibitory ones, while single neuron output is strictly positive; in line with known constraints in many biological systems. Using Dynamic Mean Field Theory, we find the phase diagram depicting the regimes of stable fixed point, unstable dynamic and chaotic rate fluctuations. We characterize the properties of systems near the chaotic transition and show that dilute excitatory-inhibitory architectures exhibit the same onset to chaos as a network with Gaussian connectivity. Interestingly, the critical properties near transition depend on the shape of the single- neuron input-output transfer function near firing threshold. Finally, we investigate network models with spiking dynamics. When synaptic time constants are slow relative to the mean inverse firing rates, the network undergoes a sharp transition from fast spiking fluctuations and static firing rates to a state with slow chaotic rate fluctuations. When the synaptic time constants are finite, the transition becomes smooth and obeys scaling properties, similar to crossover phenomena in statistical mechanicsComment: 28 Pages, 12 Figures, 5 Appendice

Synchronization in complex networks

Synchronization processes in populations of locally interacting elements are in the focus of intense research in physical, biological, chemical, technological and social systems. The many efforts devoted to understand synchronization phenomena in natural systems take now advantage of the recent theory of complex networks. In this review, we report the advances in the comprehension of synchronization phenomena when oscillating elements are constrained to interact in a complex network topology. We also overview the new emergent features coming out from the interplay between the structure and the function of the underlying pattern of connections. Extensive numerical work as well as analytical approaches to the problem are presented. Finally, we review several applications of synchronization in complex networks to different disciplines: biological systems and neuroscience, engineering and computer science, and economy and social sciences.Comment: Final version published in Physics Reports. More information available at http://synchronets.googlepages.com

Revealing networks from dynamics: an introduction

What can we learn from the collective dynamics of a complex network about its interaction topology? Taking the perspective from nonlinear dynamics, we briefly review recent progress on how to infer structural connectivity (direct interactions) from accessing the dynamics of the units. Potential applications range from interaction networks in physics, to chemical and metabolic reactions, protein and gene regulatory networks as well as neural circuits in biology and electric power grids or wireless sensor networks in engineering. Moreover, we briefly mention some standard ways of inferring effective or functional connectivity.Comment: Topical review, 48 pages, 7 figure