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

Nonlinear brain dynamics as macroscopic manifestation of underlying many-body field dynamics

Neural activity patterns related to behavior occur at many scales in time and space from the atomic and molecular to the whole brain. Here we explore the feasibility of interpreting neurophysiological data in the context of many-body physics by using tools that physicists have devised to analyze comparable hierarchies in other fields of science. We focus on a mesoscopic level that offers a multi-step pathway between the microscopic functions of neurons and the macroscopic functions of brain systems revealed by hemodynamic imaging. We use electroencephalographic (EEG) records collected from high-density electrode arrays fixed on the epidural surfaces of primary sensory and limbic areas in rabbits and cats trained to discriminate conditioned stimuli (CS) in the various modalities. High temporal resolution of EEG signals with the Hilbert transform gives evidence for diverse intermittent spatial patterns of amplitude (AM) and phase modulations (PM) of carrier waves that repeatedly re-synchronize in the beta and gamma ranges at near zero time lags over long distances. The dominant mechanism for neural interactions by axodendritic synaptic transmission should impose distance-dependent delays on the EEG oscillations owing to finite propagation velocities. It does not. EEGs instead show evidence for anomalous dispersion: the existence in neural populations of a low velocity range of information and energy transfers, and a high velocity range of the spread of phase transitions. This distinction labels the phenomenon but does not explain it. In this report we explore the analysis of these phenomena using concepts of energy dissipation, the maintenance by cortex of multiple ground states corresponding to AM patterns, and the exclusive selection by spontaneous breakdown of symmetry (SBS) of single states in sequences.Comment: 31 page

Investigating the role of fast-spiking interneurons in neocortical dynamics

PhD ThesisFast-spiking interneurons are the largest interneuronal population in neocortex. It is well documented that this population is crucial in many functions of the neocortex by subserving all aspects of neural computation, like gain control, and by enabling dynamic phenomena, like the generation of high frequency oscillations. Fast-spiking interneurons, which represent mainly the parvalbumin-expressing, soma-targeting basket cells, are also implicated in pathological dynamics, like the propagation of seizures or the impaired coordination of activity in schizophrenia. In the present thesis, I investigate the role of fast-spiking interneurons in such dynamic phenomena by using computational and experimental techniques. First, I introduce a neural mass model of the neocortical microcircuit featuring divisive inhibition, a gain control mechanism, which is thought to be delivered mainly by the soma-targeting interneurons. Its dynamics were analysed at the onset of chaos and during the phenomena of entrainment and long-range synchronization. It is demonstrated that the mechanism of divisive inhibition reduces the sensitivity of the network to parameter changes and enhances the stability and exibility of oscillations. Next, in vitro electrophysiology was used to investigate the propagation of activity in the network of electrically coupled fast-spiking interneurons. Experimental evidence suggests that these interneurons and their gap junctions are involved in the propagation of seizures. Using multi-electrode array recordings and optogenetics, I investigated the possibility of such propagating activity under the conditions of raised extracellular K+ concentration which applies during seizures. Propagated activity was recorded and the involvement of gap junctions was con rmed by pharmacological manipulations. Finally, the interaction between two oscillations was investigated. Two oscillations with di erent frequencies were induced in cortical slices by directly activating the pyramidal cells using optogenetics. Their interaction suggested the possibility of a coincidence detection mechanism at the circuit level. Pharmacological manipulations were used to explore the role of the inhibitory interneurons during this phenomenon. The results, however, showed that the observed phenomenon was not a result of synaptic activity. Nevertheless, the experiments provided some insights about the excitability of the tissue through scattered light while using optogenetics. This investigation provides new insights into the role of fast-spiking interneurons in the neocortex. In particular, it is suggested that the gain control mechanism is important for the physiological oscillatory dynamics of the network and that the gap junctions between these interneurons can potentially contribute to the inhibitory restraint during a seizure.Wellcome Trust

Cortical resting state circuits: connectivity and oscillations

Ongoing spontaneous brain activity patterns raise ever-growing interest in the neuroscience community. Complex spatiotemporal patterns that emerge from a structural core and interactions of functional dynamics have been found to be far from arbitrary in empirical studies. They are thought to compose the network structure underlying human cognitive architecture. In this thesis, we use a biophysically realistic computer model to study key factors in producing complex spatiotemporal activation patterns. For the first time, we present a model of decreased physiological signal complexity in aging and demonstrate that delays shape functional connectivity in an oscillatory spiking-neuron network model for MEG resting-state data. Our results show that the inclusion of realistic delays maximizes model performance. Furthermore, we propose embracing a datadriven, comparative stance on decomposing the system into subnetworks.Últimamente, el interés de la comunidad científica sobre los patrones de la continua actividad espontanea del cerebro ha ido en aumento. Complejos patrones espacio-temporales emergen a partir de interacciones de un núcleo estructural con dinámicas funcionales. Se ha encontrado que estos patrones no son aleatorios y que componen la red estructural en la que la arquitectura cognitiva humana se basa. En esta tesis usamos un modelo computacional detallado para estudiar los factores clave en producir los patrones emergentes. Por primera vez, presentamos un modelo simplificado de la actividad cerebral en envejecimiento. También demostramos que la inclusión del desfase de transmisión en un modelo para grabaciones magnetoencefalográficas del estado en reposo maximiza el rendimiento del modelo. Para ello, aplicamos un modelo con una red de neuronas pulsantes (’spiking-neurons’) y con dinámicas oscilatorias. Además, proponemos adoptar una posición comparativa basada en los datos para descomponer el sistema en subredes

Phase synchrony facilitates binding and segmentation of natural images in a coupled neural oscillator network

Synchronization has been suggested as a mechanism of binding distributed feature representations facilitating segmentation of visual stimuli. Here we investigate this concept based on unsupervised learning using natural visual stimuli. We simulate dual-variable neural oscillators with separate activation and phase variables. The binding of a set of neurons is coded by synchronized phase variables. The network of tangential synchronizing connections learned from the induced activations exhibits small-world properties and allows binding even over larger distances. We evaluate the resulting dynamic phase maps using segmentation masks labeled by human experts. Our simulation results show a continuously increasing phase synchrony between neurons within the labeled segmentation masks. The evaluation of the network dynamics shows that the synchrony between network nodes establishes a relational coding of the natural image inputs. This demonstrates that the concept of binding by synchrony is applicable in the context of unsupervised learning using natural visual stimuli

Modelling human choices: MADeM and decision‑making

Research supported by FAPESP 2015/50122-0 and DFG-GRTK 1740/2. RP and AR are also part of the Research, Innovation and Dissemination Center for Neuromathematics FAPESP grant (2013/07699-0). RP is supported by a FAPESP scholarship (2013/25667-8). ACR is partially supported by a CNPq fellowship (grant 306251/2014-0)

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)

Neural models of learning and visual grouping in the presence of finite conduction velocities

The hypothesis of object binding-by-synchronization in the visual cortex has been supported by recent experiments in awake monkeys. They demonstrated coherence among gamma-activities (30–90 Hz) of local neural groups and its perceptual modulation according to the rules of figure-ground segregation. Interactions within and between these neural groups are based on axonal spike conduction with finite velocities. Physiological studies confirmed that the majority of transmission delays is comparable to the temporal scale defined by gamma-activity (11–33 ms). How do these finite velocities influence the development of synaptic connections within and between visual areas? What is the relationship between the range of gamma-coherence and the velocity of signal transmission? Are these large temporal delays compatible with recently discovered phenomenon of gamma-waves traveling across larger parts of the primary visual cortex? The refinement of connections in the immature visual cortex depends on temporal Hebbian learning to adjust synaptic efficacies between spiking neurons. The impact of constant, finite, axonal spike conduction velocities on this process was investigated using a set of topographic network models. Random spike trains with a confined temporal correlation width mimicked cortical activity before visual experience. After learning, the lateral connectivity within one network layer became spatially restricted, the width of the connection profile being directly proportional to the lateral conduction velocity. Furthermore, restricted feedforward divergence developed between neurons of two successive layers. The size of this connection profile matched the lateral connection profile of the lower layer neuron. The mechanism in this network model is suitable to explain the emergence of larger receptive fields at higher visual areas while preserving a retinotopic mapping. The influence of finite conduction velocities on the local generation of gamma-activities and their spatial synchronization was investigated in a model of a mature visual area. Sustained input and local inhibitory feedback was sufficient for the emergence of coherent gamma-activity that extended across few millimeters. Conduction velocities had a direct impact on the frequency of gamma-oscillations, but did neither affect gamma-power nor the spatial extent of gamma-coherence. Adding long-range horizontal connections between excitatory neurons, as found in layer 2/3 of the primary visual cortex, increased the spatial range of gamma-coherence. The range was maximal for zero transmission delays, and for all distances attenuated with finite, decreasing lateral conduction velocities. Below a velocity of 0.5 m/s, gamma-power and gamma-coherence were even smaller than without these connections at all, i.e., slow horizontal connections actively desynchronized neural populations. In conclusion, the enhancement of gamma-coherence by horizontal excitatory connections critically depends on fast conduction velocities. Coherent gamma-activity in the primary visual cortex and the accompanying models was found to only cover small regions of the visual field. This challenges the role of gamma-synchronization to solve the binding problem for larger object representations. Further analysis of the previous model revealed that the patches of coherent gamma-activity (1.8 mm half-height decline) were part of more globally occurring gamma-waves, which coupled over much larger distances (6.3 mm half-height decline). The model gamma-waves observed here are very similar to those found in the primary visual cortex of awake monkeys, indicating that local recurrent inhibition and restricted horizontal connections with finite axonal velocities are sufficient requirements for their emergence. In conclusion, since the model is in accordance with the connectivity and gamma-processes in the primary visual cortex, the results support the hypothesis that gamma-waves provide a generalized concept for object binding in the visual cortex