Self-organized Criticality and Synchronization in a Pulse-coupled Integrate-and-Fire Neuron Model Based on Small World Networks

A lattice model for a set of pulse-coupled integrate-and-fire neurons with small world structure is introduced. We find that our model displays the power-law behavior accompanied with the large-scale synchronized activities among the units. And the different connectivity topologies lead to different behaviors in models of integrate-and-fire neurons.     

Complex Behavior in an Integrate-and-Fire Neuron Model Based on Small World Networks

Based on our previously pulse-coupled integrate-and-fire neuron model in small world networks, we investigate the complex behavior of electroencephalographic (EEG)-like activities produced by such a model. We find EEG-like activities have obvious chaotic characteristics. We also analyze the complex behaviors of EEG-like signals,such as spectral analysis, reconstruction of the phase space, the correlation dimension, and so on.     

Influence of Different Connectivity Topologies in Small World Networks Modeling Earthquakes

We introduce the Olami-Feder-Christensen (OFC) model on a square lattice with some “rewired“ longrange connections having the properties of small world networks. We find that our model displays the power-law behavior, and connectivity topologies are very important to model‘s avalanche dynamical behaviors. Our model has some behaviors different from the OFC model on a small world network with “added“ long-range connections in our previous work [LIN Min, ZHAO Xiao-Wei, and CHEN Tian-Lun, Commun. Theor. Phys. (Beijing, China) 41 (2004) 557.].     

Reliability and Efficiency of Generalized Rumor Spreading Model on Complex Social Networks

We introduce the generalized rumor spreading model and investigate some properties of this model on different complex social networks. Despite pervious rumor models that both the spreader-spreader (SS) and the spreader-stifler (SR) interactions have the same rate α, we define α⁽¹⁾ and α⁽²⁾ for SS and SR interactions, respectively. The effect of variation of α⁽¹⁾ and α⁽²⁾ on the final density of stiflers is investigated. Furthermore, the influence of the topological structure of the network in rumor spreading is studied by analyzing the behavior of several global parameters such as reliability and efficiency. Our results show that while networks with homogeneous connectivity patterns reach a higher reliability, scale-free topologies need a less time to reach a steady state with respect the rumor.     

Neuronal devices: understanding neuronal cultures through percolation helps prepare for the next step

Cultures of dissociated neurons are an invaluable experimental tool in studying neuronal networks at an intermediate scale in an in vitro controlled physico-chemical environment. Moreover, current micro-fabrication techniques allow the design of a custom connectivity between subpopulations, which could make it possible to carry out computations with devices involving living cells. The quorum percolation (QP) model has been designed in the context of neurobiology to describe bursts of activity occurring in neuronal cultures from the point of view of collective phenomena rather than from a dynamical synchronization approach. Such a model is well suited to describe triggered activity in neuronal devices, and its generic character points at the necessity of heavily structured devices to go beyond collective bursting. We derive a continuous extension of the QP model, seen as information propagation on a non-metric directed graph, and discuss how its critical behavior might give insight on the connectivity of neuronal networks. The link with metric graphs, embedded in a two-dimensional space, is tackled by the introduction of a geometrical model based upon a random walk, where axon growth is constrained by obstacles such as walls and channels. This provides a starting point for the construction of neuronal devices in vitro capable of more complex behaviors. Lastly, we show how simulations of bursts with a dynamical adaptive integrate-and-fire model can be interpreted in terms of QP, confirming the robustness of this synchronized behavior.     

Collective irregular dynamics in balanced networks of leaky integrate-and-fire neurons

We extensively explore networks of weakly unbalanced, leaky integrate-and-fire (LIF) neurons for different coupling strength, connectivity, and by varying the degree of refractoriness, as well as the delay in the spike transmission. We find that the neural network does not only exhibit a microscopic (single-neuron) stochastic-like evolution, but also a collective irregular dynamics (CID). Our analysis is based on the computation of a suitable order parameter, typically used to characterize synchronization phenomena and on a detailed scaling analysis (i.e. simulations of different network sizes). As a result, we can conclude that CID is a true thermodynamic phase, intrinsically different from the standard asynchronous regime.     

Fast response and temporal coherent oscillations in small-world networks

We have investigated the role that different connectivity regimes play in the dynamics of a network of Hodgkin-Huxley neurons by computer simulations. The different connectivity topologies exhibit the following features: random topologies give rise to fast system response yet are unable to produce coherent oscillations in the average activity of the network; on the other hand, regular topologies give rise to coherent oscillations, but in a temporal scale that is not in accordance with fast signal processing. Finally, small-world topologies, which fall between random and regular ones, take advantage of the best features of both, giving rise to fast system response with coherent oscillations.     

Self-organized Criticality in an Integrate-and-Fire Neuron Model Based on Modified Aging Networks

Based on an integrate-and-fire mechanism, we investigate self-organized criticality of a simple neuron model on a modified BA scale-free network with aging nodes. In our model, we find that the distribution of avalanche size follows power-law behavior. The critical exponent τ depends on the aging exponent α. The structures of the network with aging of nodes change with an increase of α. The different topological structures lead to different behaviors in models of integrate-and-fire neurons.     

Different Avalanche Behaviors in Different Specific Areas of a System Based on Neural Networks

Based on the standard self-organizing map (SOM) neural network model and an integrate-and-fire mecha-nism, we introduce a kind of coupled map lattice system to investigate scale-invariance behavior in the activity of model neural populations. We find power-law distribution behavior of avalanche size in our model. But more importantly, we find there are different avalanche distribution behaviors in different specific areas of our system, which are formed by the topological learning process of the SOM net.     

Different Avalanche Behaviors in Different Specific Areas of a System Based on Neural Networks

Based on the standard self-organizing map (SOM) neural network model and an integrate-and-fire mecha-nism, we introduce a kind of coupled map lattice system to investigate scale-invariance behavior in the activity of modelneural populations. We find power-law distribution behavior of avalanche size in our model. But more importantly, wefind there are different avalanche distribution behaviors in different specific areas of our system, which are formed by thetopological learning process of the SOM net.     

Estimation of the effective and functional human cortical connectivity with structural equation modeling and directed transfer function applied to high-resolution EEG

Different brain imaging devices are presently available to provide images of the human functional cortical activity, based on hemodynamic, metabolic or electromagnetic measurements. However, static images of brain regions activated during particular tasks do not convey the information of how these regions are interconnected. The concept of brain connectivity plays a central role in the neuroscience, and different definitions of connectivity, functional and effective, have been adopted in literature. While the functional connectivity is defined as the temporal coherence among the activities of different brain areas, the effective connectivity is defined as the simplest brain circuit that would produce the same temporal relationship as observed experimentally among cortical sites. The structural equation modeling (SEM) is the most used method to estimate effective connectivity in neuroscience, and its typical application is on data related to brain hemodynamic behavior tested by functional magnetic resonance imaging (fMRI), whereas the directed transfer function (DTF) method is a frequency-domain approach based on both a multivariate autoregressive (MVAR) modeling of time series and on the concept of Granger causality.

This study presents advanced methods for the estimation of cortical connectivity by applying SEM and DTF on the cortical signals estimated from high-resolution electroencephalography (EEG) recordings, since these signals exhibit a higher spatial resolution than conventional cerebral electromagnetic measures. To estimate correctly the cortical signals, we used a subject's multicompartment head model (scalp, skull, dura mater, cortex) constructed from individual MRI, a distributed source model and a regularized linear inverse source estimates of cortical current density. Before the application of SEM and DTF methodology to the cortical waveforms estimated from high-resolution EEG data, we performed a simulation study, in which different main factors (signal-to-noise ratio, SNR, and simulated cortical activity duration, LENGTH) were systematically manipulated in the generation of test signals, and the errors in the estimated connectivity were evaluated by the analysis of variance (ANOVA). The statistical analysis returned that during simulations, both SEM and DTF estimators were able to correctly estimate the imposed connectivity patterns under reasonable operative conditions, that is, when data exhibit an SNR of at least 3 and a LENGTH of at least 75 s of nonconsecutive EEG recordings at 64 Hz of sampling rate.

Hence, effective and functional connectivity patterns of cortical activity can be effectively estimated under general conditions met in any practical EEG recordings, by combining high-resolution EEG techniques and linear inverse estimation with SEM or DTF methods. We conclude that the estimation of cortical connectivity can be performed not only with hemodynamic measurements, but also with EEG signals treated with advanced computational techniques.     

Dynamic Topology Reconfiguration of Boltzmann Machines on Quantum Annealers

Boltzmann machines have useful roles in deep learning applications, such as generative data modeling, initializing weights for other types of networks, or extracting efficient representations from high-dimensional data. Most Boltzmann machines use restricted topologies that exclude looping connectivity, as such connectivity creates complex distributions that are difficult to sample. We have used an open-system quantum annealer to sample from complex distributions and implement Boltzmann machines with looping connectivity. Further, we have created policies mapping Boltzmann machine variables to the quantum bits of an annealer. These policies, based on correlation and entropy metrics, dynamically reconfigure the topology of Boltzmann machines during training and improve performance.     

Effects of Interactive Function Forms in a Self-Organized Critical Model Based on Neural Networks

Based on the standard self-organizing map neural network model and an integrate-and-fire mechanism, we introduce a kind of coupled map lattice system to investigate scale-invariance behavior in the activity of model neural populations. We let the parameter β, which together with α represents the interactive strength between neurons, have different function forms, and we find the function forms and their parameters are very important to our model‘s avalanche dynamical behaviors, especially to the emergence of different avalanche behaviors in different areas of our system.     

Effects of Interactive Function Forms in a Self-Organized Critical Model Based on Neural Networks

Based on the standard self-organizing map neural network model and an integrate-and-fire mechanism, we introduce a kind of coupled map lattice system to investigate scale-invariance behavior in the activity of model neural populations. We let the parameter β, which together with α represents the interactive strength between neurons, have different function forms, and we find the function forms and their parameters are very important to our model‘‘s avalanche dynamical behaviors, especially to the emergence of different avalanche behaviors in different areas of our system.     

Investigating the neural basis for fMRI-based functional connectivity in a blocked design: application to interregional correlations and psycho-physiological interactions

This paper investigates how well different kinds of fMRI functional connectivity analysis reflect the underlying interregional neural interactions. This is hard to evaluate using real experimental data where such relationships are unknown. Rather, we use a biologically realistic neural model to simulate both neuronal activities and multiregional fMRI data from a blocked design. Because we know how every element in the model is related to every other element, we can compare functional connectivity measurements across different spatial and temporal scales. We focus on (1) psycho-physiological interaction (PPI) analysis, which is a simple brain connectivity method that characterizes the activity in one brain region by the interaction between another region's activity and a psychological factor, and (2) interregional correlation analysis. We investigated the neurobiological underpinnings of PPI using simulated neural activities and fMRI signals generated by a large-scale neural model that performs a visual delayed match-to-sample task. Simulated fMRI data are generated by convolving integrated synaptic activities (ISAs) with a hemodynamic response function. The simulation was done under three task conditions: high-attention, low-attention and a control task ('passive viewing'). We investigated how biological and scanning parameters affect PPI and compared these with functional connectivity measures obtained using correlation analysis. We performed correlational and PPI analyses with three types of time-series data: ISA, fMRI and deconvolved fMRI (which yields estimated neural signals) obtained using a deconvolution algorithm. The simulated ISA can be considered as the 'gold standard' because it represents the underlying neural activity. Our main findings show (1) that evaluating the change in an interregional functional connection using the difference in regression coefficients (as is essentially done in the PPI method) produces results that better reflect the underlying changes in neural interrelationships than does evaluating the functional connectivity difference as a change in correlation coefficient; (2) that using fMRI and deconvolved fMRI data led to similar conclusions in the PPI-based functional connectivity results, and these generally agreed with the nature of the underlying neural interactions; and (3) the functional connectivity correlation measures often led to different conclusions regarding significance for different scanning and hemodynamic parameters, but the significances of the PPI regression parameters were relatively robust. These results highlight the way in which neural modeling can be used to help validate the inferences one can make about functional connectivity based on fMRI data.     

Amplified signal response in scale-free networks by collaborative signaling

Many natural and artificial two-states signaling devices are connected forming networks. The information-processing potential of these systems is usually related to the response to weak external signals. Here, using a network of overdamped bistable elements, we study the effect of a heterogeneous complex topology on the signal response. The analysis of the problem in random scale-free networks, reveals that heterogeneity plays a crucial role in amplifying external signals. We have contrasted numerical simulations with analytical calculations in simplified topologies.     

Tour time in a two-route traffic system controlled by signals

We study the dynamic behavior of vehicular traffic in a two-route system with a series of signals (traffic lights) at low density where the number of signals on route A is different from that on route B. We investigate the dependence of the tour time on the route for some strategies of signal control. The nonlinear dynamic model of a two-route traffic system controlled by signals is presented by nonlinear maps. The vehicular traffic exhibits a very complex behavior, depending on the cycle time, the phase difference, and the irregularity. The dependence of the tour time on the route choice is clarified for the signal strategies.     

Effects of strong coupling in homonuclear correlation spectroscopy

A calculation of the complex signals in homonuclear correlation spectra (HOMCOR) of strongly coupled ABX three-spin systems is presented. It is shown that the presence of strong coupling causes the behavior of the cross-peaks to differ significantly from that found in the case of weak coupling. Two classes of connectivity patterns, namely weak and strong connectivity pairs of transitions are distinguished. Closed expressions for the real amplitudes are given. The dependence of the real amplitude on the flip angle of the mixing pulse and on the coupling strength is analyzed.     

Microgels and fractal structures at interfaces and surfaces

The behavior of microgels near surfaces and their adsorption is studied by simple scaling theory. Two different types of microgels can be studied, i.e., fractal type microgels and randomly crosslinked polymer chains. In the first case the gel can be described mainly by introducing a spectral dimension. The second type requires more attention and uses the number of crosslinks as parameter. The main result is that soft gels with weakly coupled crosslinks and a low number of crosslinks adsorb much better than hard gels, with many crosslinks. Similar results for fractal gels and branched polymer are presented. Fractal gels with low connectivity adsorb easier than gels with a large connectivity dimension. We discuss also consequences on surface protection by microgels. Received: 11 August 1997 / Received in final form: 20 November 1997 / Accepted 22 January 1998     

Speed of synchronization in complex networks of neural oscillators: analytic results based on Random Matrix Theory

We analyze the dynamics of networks of spiking neural oscillators. First, we present an exact linear stability theory of the synchronous state for networks of arbitrary connectivity. For general neuron rise functions, stability is determined by multiple operators, for which standard analysis is not suitable. We describe a general nonstandard solution to the multioperator problem. Subsequently, we derive a class of neuronal rise functions for which all stability operators become degenerate and standard eigenvalue analysis becomes a suitable tool. Interestingly, this class is found to consist of networks of leaky integrate-and-fire neurons. For random networks of inhibitory integrate-and-fire neurons, we then develop an analytical approach, based on the theory of random matrices, to precisely determine the eigenvalue distributions of the stability operators. This yields the asymptotic relaxation time for perturbations to the synchronous state which provides the characteristic time scale on which neurons can coordinate their activity in such networks. For networks with finite in-degree, i.e., finite number of presynaptic inputs per neuron, we find a speed limit to coordinating spiking activity. Even with arbitrarily strong interaction strengths neurons cannot synchronize faster than at a certain maximal speed determined by the typical in-degree.