Scale-free Connectivity Research Articles

Modeling the three-dimensional connectivity of in vitro cortical ensembles coupled to Micro-Electrode Arrays.

Nowadays, in vitro three-dimensional (3D) neuronal networks are becoming a consolidated experimental model to overcome most of the intrinsic limitations of bi-dimensional (2D) assemblies. In the 3D environment, experimental evidence revealed a wider repertoire of activity patterns, characterized by a modulation of the bursting features, than the one observed in 2D cultures. However, it is not totally clear and understood what pushes the neuronal networks towards different dynamical regimes. One possible explanation could be the underlying connectivity, which could involve a larger number of neurons in a 3D rather than a 2D space and could organize following well-defined topological schemes. Driven by experimental findings, achieved by recording 3D cortical networks organized in multi-layered structures coupled to Micro-Electrode Arrays (MEAs), in the present work we developed a large-scale computational network model made up of leaky integrate-and-fire (LIF) neurons to investigate possible structural configurations able to sustain the emerging patterns of electrophysiological activity. In particular, we investigated the role of the number of layers defining a 3D assembly and the spatial distribution of the connections within and among the layers. These configurations give rise to different patterns of activity that could be compared to the ones emerging from real in vitro 3D neuronal populations. Our results suggest that the introduction of three-dimensionality induced a global reduction in both firing and bursting rates with respect to 2D models. In addition, we found that there is a minimum number of layers necessary to obtain a change in the dynamics of the network. However, the effects produced by a 3D organization of the cells is somewhat mitigated if a scale-free connectivity is implemented in either one or all the layers of the network. Finally, the best matching of the experimental data is achieved supposing a 3D connectivity organized in structured bundles of links located in different areas of the 2D network.

Scale-Free Functional Brain Networks Exhibit Increased Connectivity, Are More Integrated and Less Segregated in Patients with Parkinson's Disease following Dopaminergic Treatment.

Dopaminergic treatment (DT), the standard therapy for Parkinson's disease (PD), alters the dynamics of functional brain networks at specific time scales. Here, we explore the scale-free functional connectivity (FC) in the PD population and how it is affected by DT. We analyzed the electroencephalogram of: (i) 15 PD patients during DT (ON) and after DT washout (OFF) and (ii) 16 healthy control individuals (HC). We estimated FC using bivariate focus-based multifractal analysis, which evaluated the long-term memory and multifractal strength of the connections. Subsequent analysis yielded network metrics (node degree, clustering coefficient and path length) based on FC estimated by or . Cognitive performance was assessed by the Mini Mental State Examination (MMSE) and the North American Adult Reading Test (NAART). The node degrees of the networks were significantly higher in ON, compared to OFF and HC, while clustering coefficient and path length significantly decreased. No alterations were observed in the networks. Significant positive correlations were also found between the metrics of networks and NAART scores in the HC group. These results demonstrate that DT alters the multifractal coupled dynamics in the brain, warranting the investigation of scale-free FC in clinical and pharmacological studies.

Quantitative analysis and spatial distribution of landform spatial structure on Loess Plateau

The Loess Plateau is the largest gully geomorphic region in the world, characterized by the most intense soil erosion in a typical loess-covered area. Previous studies have focused on the terrain and texture of this region; however, there have been no systematic studies on the gully spatial structure of the Loess Plateau. Therefore, the present study investigated the characteristics and spatial distribution of landform spatial structure over the Loess Plateau. Specifically, gully weighted complex networks (GWCNs) were applied to simulate the gully spatial structure of loess landforms, and a series of quantitative indices were introduced to delineate these. Using 57 geomorphological units uniformly distributed across the Loess Plateau as test areas and six typical loess landforms as sample areas, GWCNs were constructed, and using these GWCNs, the spatial structure and internal mechanisms of typical loess landforms were explored. From a series of fresh insights, such as the regional scale-free distribution, homologous structure, tightness, community effect, connectivity, stability, and complexity, regular variations in quantitative indices delineate the spatial distribution of the characteristics of landform spatial structure over the plateau. Moreover, the spatial distribution of complex network indices exhibited strong spatial coupling with loess landforms. Overall, GWCNs could be effectively used for landform recognition and performed well. In conclusion, these experimental results suggest that introducing complex networks into landform studies can offer novel insights into landform quantitative analyses. The present work is of great significance, as it proposes a new methodology for describing the spatial structure and terrain features of landforms in quantitative analyses and furthers our understanding of landform genesis.

Multiple-Resampling Cross-Spectral Analysis: An Unbiased Tool for Estimating Fractal Connectivity With an Application to Neurophysiological Signals.

Investigating scale-free (i.e., fractal) functional connectivity in the brain has recently attracted increasing attention. Although numerous methods have been developed to assess the fractal nature of functional coupling, these typically ignore that neurophysiological signals are assemblies of broadband, arrhythmic activities as well as oscillatory activities at characteristic frequencies such as the alpha waves. While contribution of such rhythmic components may bias estimates of fractal connectivity, they are also likely to represent neural activity and coupling emerging from distinct mechanisms. Irregular-resampling auto-spectral analysis (IRASA) was recently introduced as a tool to separate fractal and oscillatory components in the power spectrum of neurophysiological signals by statistically summarizing the power spectra obtained when resampling the original signal by several non-integer factors. Here we introduce multiple-resampling cross-spectral analysis (MRCSA) as an extension of IRASA from the univariate to the bivariate case, namely, to separate the fractal component of the cross-spectrum between two simultaneously recorded neural signals by applying the same principle. MRCSA does not only provide a theoretically unbiased estimate of the fractal cross-spectrum (and thus its spectral exponent) but also allows for computing the proportion of scale-free coupling between brain regions. As a demonstration, we apply MRCSA to human electroencephalographic recordings obtained in a word generation paradigm. We show that the cross-spectral exponent as well as the proportion of fractal coupling increases almost uniformly over the cortex during the rest-task transition, likely reflecting neural desynchronization. Our results indicate that MRCSA can be a valuable tool for scale-free connectivity studies in characterizing various cognitive states, while it also can be generalized to other applications outside the field of neuroscience.

Flipping the switch on the hub cell: Islet desynchronization through cell silencing.

Pancreatic β cells, responsible for secreting insulin into the bloodstream and maintaining glucose homeostasis, are organized in the islets of Langerhans as clusters of electrically coupled cells. Gap junctions, connecting neighboring cells, coordinate the behavior of the islet, leading to the synchronized oscillations in the intracellular calcium and insulin secretion in healthy islets. Recent experimental work has shown that silencing special hub cells can lead to a disruption in the coordinated behavior, calling into question the democratic paradigm of islet insulin secretion with more or less equal input from each β cell. Islets were shown to have scale-free functional connectivity and a hub cell whose silencing would lead to a loss of functional connectivity and activity in the islet. A mechanistic model representing the electrical and calcium dynamics of β cells during insulin secretion was applied to a network of cells connected by gap junctions to test the hypothesis of hub cells. Functional connectivity networks were built from the simulated calcium traces, with some networks classified as scale-free, confirming experimental results. Potential hub cells were identified using previously defined centrality measures, but silencing them was unable to desynchronize the islet. Instead, switch cells, which were able to turn off the activity of the islet but were not highly functionally connected, were found via systematically silencing each cell in the network.

Dynamical Features of a Focal Epileptogenic Network Model for Stimulation-Based Control.

Much attention has been dedicated to clinical research of focal epilepsy, but the ability to derive a successful seizure control strategy based on unique dynamical features of the electroencephalogram is an unsolved problem. In this work, we introduce a basic model of spontaneous seizure dynamics and construct from it to a network model of focal-onset seizure dynamics. The full model is composed of coupled oscillators with scale-free network connectivity and a common slow variable. We find that global parameter changes and variation of the connectivity can drive the model from a quiescent state to recurrent seizures, and, eventually, to a permanent-seizure-state. Based on network synchronization features we design a stimulation scheme for the control of the fraction of nodes with strongest phase locking is proposed. Simulations lead to the identification of optimal stimuli for a given type of dynamics. Our results contribute to the development of a rational strategy for the non-surgical treatment of drug-resistant epilepsy.

Metabolite-Centric Reporter Pathway and Tripartite Network Analysis of Arabidopsis Under Cold Stress.

The study of plant resistance to cold stress and the metabolic processes underlying its molecular mechanisms benefit crop improvement programs. Here we investigate the effects of cold stress on the metabolic pathways of Arabidopsis when directly inferred at system level from transcriptome data. A metabolite-centric reporter pathway analysis approach enabled the computation of metabolites associated with transcripts at four time points of cold treatment. Tripartite networks of gene-metabolite-pathway connectivity outlined the response of metabolites and pathways to cold stress. Our metabolome-independent analysis revealed stress-associated metabolites in pathway routes of the cold stress response, including amino acid, carbohydrate, lipid, hormone, energy, photosynthesis, and signaling pathways. Cold stress first triggered the mobilization of energy from glycolysis and ethanol degradation to enhance TCA cycle activity via acetyl-CoA. Interestingly, tripartite networks lacked power law behavior and scale free connectivity, favoring modularity. Network rewiring explicitly involved energetics, signal, carbon and redox metabolisms and membrane remodeling.

Modular co-organization of functional connectivity and scale-free dynamics in the human brain.

Scale-free neuronal dynamics and interareal correlations are emergent characteristics of spontaneous brain activity. How such dynamics and the anatomical patterns of neuronal connectivity are mutually related in brain networks has, however, remained unclear. We addressed this relationship by quantifying the network colocalization of scale-free neuronal activity—both neuronal avalanches and long-range temporal correlations (LRTCs)—and functional connectivity (FC) by means of intracranial and noninvasive human resting-state electrophysiological recordings. We found frequency-specific colocalization of scale-free dynamics and FC so that the interareal couplings of LRTCs and the propagation of neuronal avalanches were most pronounced in the predominant pathways of FC. Several control analyses and the frequency specificity of network colocalization showed that the results were not trivial by-products of either brain dynamics or our analysis approach. Crucially, scale-free neuronal dynamics and connectivity also had colocalized modular structures at multiple levels of network organization, suggesting that modules of FC would be endowed with partially independent dynamic states. These findings thus suggest that FC and scale-free dynamics—hence, putatively, neuronal criticality as well—coemerge in a hierarchically modular structure in which the modules are characterized by dense connectivity, avalanche propagation, and shared dynamic states.

Effect of network architecture on burst and spike synchronization in a scale-free network of bursting neurons

We investigate the effect of network architecture on burst and spike synchronization in a directed scale-free network (SFN) of bursting neurons, evolved via two independent α- and β-processes. The α-process corresponds to a directed version of the Barabási–Albert SFN model with growth and preferential attachment, while for the β-process only preferential attachments between pre-existing nodes are made without addition of new nodes. We first consider the “pure” α-process of symmetric preferential attachment (with the same in- and out-degrees), and study emergence of burst and spike synchronization by varying the coupling strength J and the noise intensity D for a fixed attachment degree. Characterizations of burst and spike synchronization are also made by employing realistic order parameters and statistical-mechanical measures. Next, we choose appropriate values of J and D where only burst synchronization occurs, and investigate the effect of the scale-free connectivity on the burst synchronization by varying (1) the symmetric attachment degree and (2) the asymmetry parameter (representing deviation from the symmetric case) in the α-process, and (3) the occurrence probability of the β-process. In all these three cases, changes in the type and the degree of population synchronization are studied in connection with the network topology such as the degree distribution, the average path length Lp, and the betweenness centralization Bc. It is thus found that just taking into consideration Lp and Bc (affecting global communication between nodes) is not sufficient to understand emergence of population synchronization in SFNs, but in addition to them, the in-degree distribution (affecting individual dynamics) must also be considered to fully understand for the effective population synchronization.

How different connectivity patterns of individuals within an organization can speed up organizational learning

Knowledge sharing within a cooperative organization is an important issue since the power of its outcome has been the principal source of competitive advantage over the competitors in the market. However, without a proper collective knowledge management, its utilization as a strategic weapon or competitive advantage becomes difficult and inefficient. From an organizational perspective, the most important aspect of knowledge management is to transfer knowledge. In this regards, organizations must adopt structures that allow them to create and transfer more knowledge. Organizational communication structure affects the nature of human interactions and information flow which in its own turn can lead to a competitive advantage in the knowledge economy. However, in addition to that, social relationships between individuals in an organization can also be utilized to produce positive returns. In this article we emphasize the role of individual structural importance within an organizational informal communication structure as a mechanism for knowledge flow and speeding up organizational learning. Our experimental results indicate the fact that structural position of individuals within their informal communication networks can help the network members to have a better access to ongoing information exchange processes in the organization. The results of our analyses also show that organizational learning through an informal communication network of people in the form of scale-free connectivity pattern is faster comparing to the small-world connectivity style.

Size, connectivity, and tipping in spatial networks: Theory and empirics

We study the impact of settlement sizes on network connectivity in a spatial setting. First, we develop a model of geometric urban networks that posits a positive relationship between connectivity and size. Empirical evidence is then presented validating the model prediction that local links exhibit super-linear scaling with the exponent greater than 1, while long-range connections scale linearly with the unit exponent. The scaling exponents thus suggest that the impact of population size on connectivity is stronger within cities than between cities. We next combine the geometric framework with a computational model of interacting agents to generate a realistic settlement distribution and urban networks from the bottom-up. Calibrated simulation results demonstrate the consistency between hierarchical rank-size distribution and scale-free connectivity. Finally, coupling the spatial network with a tipping diffusion model allows us to consolidate the evolution of network connectivity, city sizes, and social practices in a unified computational framework.

Percolation and Scale-Free Connectivity for Wireless Sensor Networks

Based on complex network analysis and percolation theory, this letter proposes a method called LTPT to generate scale-free topology for wireless sensor networks (WSNs), with required connectivity and lifetime. The problem is divided into logical topology (LT) and physical topology (PT) analysis. With LTPT, we generate a robust logical topology of power-law degree distribution and build a physical topology of guaranteed connectivity and lifetime. This is the first time the connection between logical and physical connectivities is set up analytically.

How Do Investment Ideas Spread through Social Interaction? Evidence from a Ponzi Scheme

A unique dataset from a large Ponzi scheme shows that investment ideas can spread epidemically through social contagion. Investors could join the scheme only by personal invitation from an existing member, and I can observe how the idea spreads from one person to the next based on the inviter-invitee relationships. The social network has so-called scale-free connectivity structure where the distribution of the number of invited people approximately follows a power law. The structure differs significantly from randomly formed networks and explains why word-of-mouth information can spread rapidly even if the average investor does not share it with many others.

Heterogeneity of heterogeneities in neuronal networks.

Heterogeneity of heterogeneities in neuronal networks.

Effects of Spike Frequency Adaptation on Synchronization Transitions in Electrically Coupled Neuronal Networks with Scale-Free Connectivity

Effects of spike frequency adaptation (SFA) on the synchronous behavior of population neurons are investigated in electrically coupled networks with a scale-free property. By a computational approach, we corroborate that pairwise correlations between neurons would decrease if neurons exhibit the feature of SFA, which is similar to previous experimental observations. However, unlike the case of pairwise correlations, population activities of neurons show a rather complex variation mode: compared with those of non-adapted neurons, neurons in the networks having weak-degrees of SFA will impair population synchronizations; while neurons exhibiting strong-degrees of SFA will enhance population synchronizations. Moreover, a variation of coupling strength between neurons will not alter this phenomenon significantly, unless the coupling strength is too weak. Our results suggest that synchronous activity of electrically coupled population neurons is adaptation-dependent, and this adaptive feature may imply some coding strategies of neuronal populations.

Scale-Free Functional Connectivity of the Brain Is Maintained in Anesthetized Healthy Participants but Not in Patients with Unresponsive Wakefulness Syndrome

Loss of consciousness in anesthetized healthy participants and in patients with unresponsive wakefulness syndrome (UWS) is associated with substantial alterations of functional connectivity across large-scale brain networks. Yet, a prominent distinction between the two cases is that after anesthesia, brain connectivity and consciousness are spontaneously restored, whereas in patients with UWS this restoration fails to occur, but why? A possible explanation is that the self-organizing capability of the brain is compromised in patients with UWS but not in healthy participants undergoing anesthesia. According to the theory of self-organized criticality, many natural complex systems, including the brain, evolve spontaneously to a critical state wherein system behaviors display spatial and/or temporal scale-invariant characteristics. Here we tested the hypothesis that the scale-free property of brain network organization is in fact fundamentally different between anesthetized healthy participants and UWS patients. We introduced a novel, computationally efficient approach to determine anatomical-functional parcellation of the whole-brain network at increasingly finer spatial scales. We found that in healthy participants, scale-free distributions of node size and node degree were present across wakefulness, propofol sedation, and recovery, despite significant propofol-induced functional connectivity changes. In patients with UWS, the scale-free distribution of node degree was absent, reflecting a fundamental difference between the two groups in adaptive reconfiguration of functional interaction between network components. The maintenance of scale-invariance across propofol sedation in healthy participants suggests the presence of persistent, on-going self-organizing processes to a critical state – a capacity that is compromised in patients with UWS.

The emergence of mind and emotion in the evolution of neocortex.

The most deeply transformative concept for the growth of 21st Century psychiatry is the constellation of the chaotic dynamics of the brain. Brains are no longer seen as rational systems that are plagued with emotional disorders reflecting primitives inherited from our animal ancestors. Brains are dynamical systems that continually create patterns by acting intentionally into the environment and shaping themselves in accord with the sensory consequences of their intended actions. Emotions are now seen not as reversions to animal behaviors but as the sources of force and energy that brains require for the actions they take to understand the world and themselves. Humans are unique in experiencing consciousness of their own actions, which they experience as conscience: guilt, shame, pride and joy. Chaotic brain dynamics strives always for unity and harmony, but as a necessary condition for adaptation to a changing world, it repeatedly lapses into disorder. The successes are seen in the normal unity of consciousness; the failures are seen in the disorders that we rightly label the schizophrenias and the less severe character disorders. The foundation for healthy unity is revealed by studies in the evolution of brains, in particular the way in which neocortex of mammals emerged from the primitive allocortex of reptiles. The amazing facts of brain dynamics are now falling into several places. The power-law connectivity of cortex supports the scale-free dynamics of the global workspace in brains ranging from mouse to whale. That dynamics in humans holds the secrets of speech and symbol utilization. By recursive interactions in vast areas of human neocortex the scale-free connectivity supports our unified consciousness. Here in this dynamics are to be sought the keys to understanding and treating the disorders that uniquely plague the human mind.

Topological effects on dynamics in complex pulse-coupled networks of integrate-and-fire type

For a class of integrate-and-fire, pulse-coupled networks with complex topology, we study the dependence of the pulse rate on the underlying architectural connectivity statistics. We derive the distribution of the pulse rate from this dependence and determine when the underlying scale-free architectural connectivity gives rise to a scale-free pulse-rate distribution. We identify the scaling of the pairwise coupling between the dynamical units in this network class that keeps their pulse rates bounded in the infinite-network limit. In the process, we determine the connectivity statistics for a specific scale-free network grown by preferential attachment.

Connectivity and thought: The influence of semantic network structure in a neurodynamical model of thinking

Understanding cognition has been a central focus for psychologists, neuroscientists and philosophers for thousands of years, but many of its most fundamental processes remain very poorly understood. Chief among these is the process of thought itself: the spontaneous emergence of specific ideas within the stream of consciousness. It is widely accepted that ideas, both familiar and novel, arise from the combination of existing concepts. From this perspective, thought is an emergent attribute of memory, arising from the intrinsic dynamics of the neural substrate in which information is embedded. An important issue in any understanding of this process is the relationship between the emergence of conceptual combinations and the dynamics of the underlying neural networks. Virtually all theories of ideation hypothesize that ideas arise during the thought process through association, each one triggering the next through some type of linkage, e.g., structural analogy, semantic similarity, polysemy, etc. In particular, it has been suggested that the creativity of ideation in individuals reflects the qualitative structure of conceptual associations in their minds. Interestingly, psycholinguistic studies have shown that semantic networks across many languages have a particular type of structure with small-world, scale free connectivity. So far, however, these related insights have not been brought together, in part because there has been no explicitly neural model for the dynamics of spontaneous thought. Recently, we have developed such a model. Though simplistic and abstract, this model attempts to capture the most basic aspects of the process hypothesized by theoretical models within a neurodynamical framework. It represents semantic memory as a recurrent semantic neural network with itinerant dynamics. Conceptual combinations arise through this dynamics as co-active groups of neural units, and either dissolve quickly or persist for a time as emergent metastable attractors and are recognized consciously as ideas. The work presented in this paper describes this model in detail, and uses it to systematically study the relationship between the structure of conceptual associations in the neural substrate and the ideas arising from this system's dynamics. In particular, we consider how the small-world and scale-free characteristics influence the effectiveness of the thought process under several metrics, and show that networks with both attributes indeed provide significant advantages in generating unique conceptual combinations.

Emergence of features in protein-protein interaction networks

Scale-free connectivity, small-world pattern, hierarchical modularity and disassortative mixing are prominent features shared by most biological networks. Up to now, various network growth models invoking gene duplication and divergence have been proposed to understand the evolutionary mechanisms shaping the scale-free connectivity, small-world pattern and disassortative mixing . In this paper, we present an evolutionary model by introducing a rule of small preference duplication of a node and sequently divergence plus non-uniform heterodimerization meaning that the probability that an heterodimerization link is added between duplicated nodes is proportional to the number of common neighbors shared by these nodes based on biological background, showing that our model can almost display series of topological characteristics of real protein interaction networks, such as scale-free connectivity, small-world pattern, disassortativity of degree-degree correlation and hierarchical modularity. Our model may yield relevant insights into the evolutionary mechanism of protein interaction networks behind it.