Network catastrophe: self-organized patterns reveal both the instability and the structure of complex networks.
ABSTRACT: Critical events in society or biological systems can be understood as large-scale self-emergent phenomena due to deteriorating stability. We often observe peculiar patterns preceding these events, posing a question of-how to interpret the self-organized patterns to know more about the imminent crisis. We start with a very general description - of interacting population giving rise to large-scale emergent behaviors that constitute critical events. Then we pose a key question: is there a quantifiable relation between the network of interactions and the emergent patterns? Our investigation leads to a fundamental understanding to: 1. Detect the system's transition based on the principal mode of the pattern dynamics; 2. Identify its evolving structure based on the observed patterns. The main finding of this study is that while the pattern is distorted by the network of interactions, its principal mode is invariant to the distortion even when the network constantly evolves. Our analysis on real-world markets show common self-organized behavior near the critical transitions, such as housing market collapse and stock market crashes, thus detection of critical events before they are in full effect is possible.
Project description:Self-organized spatial patterns occur in many terrestrial, aquatic, and marine ecosystems. Theoretical models and observational studies suggest self-organization, the formation of patterns due to ecological interactions, is critical for enhanced ecosystem resilience. However, experimental tests of this cross-ecosystem theory are lacking. In this study, we experimentally test the hypothesis that self-organized pattern formation improves the persistence of mussel beds (Mytilus edulis) on intertidal flats. In natural beds, mussels generate self-organized patterns at two different spatial scales: regularly spaced clusters of mussels at centimeter scale driven by behavioral aggregation and large-scale, regularly spaced bands at meter scale driven by ecological feedback mechanisms. To test for the relative importance of these two spatial scales of self-organization on mussel bed persistence, we conducted field manipulations in which we factorially constructed small-scale and/or large-scale patterns. Our results revealed that both forms of self-organization enhanced the persistence of the constructed mussel beds in comparison to nonorganized beds. Small-scale, behaviorally driven cluster patterns were found to be crucial for persistence, and thus resistance to wave disturbance, whereas large-scale, self-organized patterns facilitated reformation of small-scale patterns if mussels were dislodged. This study provides experimental evidence that self-organization can be paramount to enhancing ecosystem persistence. We conclude that ecosystems with self-organized spatial patterns are likely to benefit greatly from conservation and restoration actions that use the emergent effects of self-organization to increase ecosystem resistance to disturbance.
Project description:<h4>Background</h4>Neurons are dynamically coupled with each other through neurite-mediated adhesion during development. Understanding the collective behavior of neurons in circuits is important for understanding neural development. While a number of genetic and activity-dependent factors regulating neuronal migration have been discovered on single cell level, systematic study of collective neuronal migration has been lacking. Various biological systems are shown to be self-organized, and it is not known if neural circuit assembly is self-organized. Besides, many of the molecular factors take effect through spatial patterns, and coupled biological systems exhibit emergent property in response to geometric constraints. How geometric constraints of the patterns regulate neuronal migration and circuit assembly of neurons within the patterns remains unexplored.<h4>Methodology/principal findings</h4>We established a two-dimensional model for studying collective neuronal migration of a circuit, with hippocampal neurons from embryonic rats on Matrigel-coated self-assembled monolayers (SAMs). When the neural circuit is subject to geometric constraints of a critical scale, we found that the collective behavior of neuronal migration is spatiotemporally coordinated. Neuronal somata that are evenly distributed upon adhesion tend to aggregate at the geometric center of the circuit, forming mono-clusters. Clustering formation is geometry-dependent, within a critical scale from 200 µm to approximately 500 µm. Finally, somata clustering is neuron-type specific, and glutamatergic and GABAergic neurons tend to aggregate homo-philically.<h4>Conclusions/significance</h4>We demonstrate self-organization of neural circuits in response to geometric constraints through spatiotemporally coordinated neuronal migration, possibly via mechanical coupling. We found that such collective neuronal migration leads to somata clustering, and mono-cluster appears when the geometric constraints fall within a critical scale. The discovery of geometry-dependent collective neuronal migration and the formation of somata clustering in vitro shed light on neural development in vivo.
Project description:<h4>Background</h4>The experimental observations and numerical studies with dissipative metabolic networks have shown that cellular enzymatic activity self-organizes spontaneously leading to the emergence of a Systemic Metabolic Structure in the cell, characterized by a set of different enzymatic reactions always locked into active states (metabolic core) while the rest of the catalytic processes are only intermittently active. This global metabolic structure was verified for Escherichia coli, Helicobacter pylori and Saccharomyces cerevisiae, and it seems to be a common key feature to all cellular organisms. In concordance with these observations, the cell can be considered a complex metabolic network which mainly integrates a large ensemble of self-organized multienzymatic complexes interconnected by substrate fluxes and regulatory signals, where multiple autonomous oscillatory and quasi-stationary catalytic patterns simultaneously emerge. The network adjusts the internal metabolic activities to the external change by means of flux plasticity and structural plasticity.<h4>Methodology/principal findings</h4>In order to research the systemic mechanisms involved in the regulation of the cellular enzymatic activity we have studied different catalytic activities of a dissipative metabolic network under different external stimuli. The emergent biochemical data have been analysed using statistical mechanic tools, studying some macroscopic properties such as the global information and the energy of the system. We have also obtained an equivalent Hopfield network using a Boltzmann machine. Our main result shows that the dissipative metabolic network can behave as an attractor metabolic network.<h4>Conclusions/significance</h4>We have found that the systemic enzymatic activities are governed by attractors with capacity to store functional metabolic patterns which can be correctly recovered from specific input stimuli. The network attractors regulate the catalytic patterns, modify the efficiency in the connection between the multienzymatic complexes, and stably retain these modifications. Here for the first time, we have introduced the general concept of attractor metabolic network, in which this dynamic behavior is observed.
Project description:In social systems ranging from ant colonies to human society, behavioural specialization-consistent individual differences in behaviour-is commonplace: individuals can specialize in the tasks they perform (division of labour (DOL)), the political behaviour they exhibit (political polarization) or the non-task behaviours they exhibit (personalities). Across these contexts, behavioural specialization often co-occurs with modular and assortative social networks, such that individuals tend to associate with others that have the same behavioural specialization. This raises the question of whether a common mechanism could drive co-emergent behavioural specialization and social network structure across contexts. To investigate this question, here we extend a model of self-organized DOL to account for social influence and interaction bias among individuals-social dynamics that have been shown to drive political polarization. We find that these same social dynamics can also drive emergent DOL by forming a feedback loop that reinforces behavioural differences between individuals, a feedback loop that is impacted by group size. Moreover, this feedback loop also results in modular and assortative social network structure, whereby individuals associate strongly with those performing the same task. Our findings suggest that DOL and political polarization-two social phenomena not typically considered together-may actually share a common social mechanism. This mechanism may result in social organization in many contexts beyond task performance and political behaviour.
Project description:Neuronal avalanches measured in vitro and in vivo in different cortical networks consistently exhibit power law behaviour for the size and duration distributions with exponents typical for a mean field self-organized branching process. These exponents are also recovered in neuronal network simulations implementing various neuronal dynamics on different network topologies. They can therefore be considered a very robust feature of spontaneous neuronal activity. Interestingly, this scaling behaviour is also observed on regular lattices in finite dimensions, which raises the question about the origin of the mean field behavior observed experimentally. In this study we provide an answer to this open question by investigating the effect of activity dependent plasticity in combination with the neuronal refractory time in a neuronal network. Results show that the refractory time hinders backward avalanches forcing a directed propagation. Hebbian plastic adaptation plays the role of sculpting these directed avalanche patterns into the topology of the network slowly changing it into a branched structure where loops are marginal.
Project description:Self-organization and pattern formation in network-organized systems emerges from the collective activation and interaction of many interconnected units. A striking feature of these non-equilibrium structures is that they are often localized and robust: only a small subset of the nodes, or cell assembly, is activated. Understanding the role of cell assemblies as basic functional units in neural networks and socio-technical systems emerges as a fundamental challenge in network theory. A key open question is how these elementary building blocks emerge, and how they operate, linking structure and function in complex networks. Here we show that a network analogue of the Swift-Hohenberg continuum model-a minimal-ingredients model of nodal activation and interaction within a complex network-is able to produce a complex suite of localized patterns. Hence, the spontaneous formation of robust operational cell assemblies in complex networks can be explained as the result of self-organization, even in the absence of synaptic reinforcements.
Project description:The development of selective visual attention is critical for effectively engaging with an ever-changing world. Its optimal deployment depends upon interactions between neural, motor, and sensory systems across multiple timescales and neurocognitive loci. Previous work illustrates the spatio-temporal dynamics of these processes in adults, but less is known about this emergent phenomenon early in life. Using data (n?=?190; 421 visits) collected between 3 and 35 months of age, we examined the spatio-temporal complexity of young children's gaze patterns as they viewed stimuli varying in semantic salience. Specifically, we used detrended fluctuation analysis (DFA) to quantify the extent to which infants' gaze patterns exhibited scale invariant patterns of nested variability, an organizational feature thought to reflect self-organized and optimally flexible system dynamics that are not overly rigid or random. Results indicated that gaze patterns of even the youngest infants exhibited fractal organization that increased with age. Further, fractal organization was greater when children (a) viewed social stimuli compared to stimuli with degraded social information and (b) when they spontaneously gazed at faces. These findings suggest that selective attention is well-organized in infancy, particularly toward social information, and indicate noteworthy growth in these processes across the first years of life.
Project description:Improved therapy of brain disorders can be achieved by focusing on neuronal networks, utilizing combined pharmacological and stimulation paradigms guided by neuroimaging. Neuronal networks that mediate normal brain functions, such as hearing, interact with other networks, which is important but commonly neglected. Network interaction changes often underlie brain disorders, including epilepsy. "Conditional multireceptive" (CMR) brain areas (e.g., brainstem reticular formation and amygdala) are critical in mediating neuroplastic changes that facilitate network interactions. CMR neurons receive multiple inputs but exhibit extensive response variability due to milieu and behavioral state changes and are exquisitely sensitive to agents that increase or inhibit GABA-mediated inhibition. Enhanced CMR neuronal responsiveness leads to expression of emergent properties--nonlinear events--resulting from network self-organization. Determining brain disorder mechanisms requires animals that model behaviors and neuroanatomical substrates of human disorders identified by neuroimaging. However, not all sites activated during network operation are requisite for that operation. Other active sites are ancillary, because their blockade does not alter network function. Requisite network sites exhibit emergent properties that are critical targets for pharmacological and stimulation therapies. Improved treatment of brain disorders should involve combined pharmacological and stimulation therapies, guided by neuroimaging, to correct network malfunctions by targeting specific network neurons.
Project description:In vertebrate embryos, somites, the precursor of vertebrae, form from the presomitic mesoderm (PSM), which is composed of cells displaying signaling oscillations. Cellular oscillatory activity leads to periodic wave patterns in the PSM. Here, we address the origin of such complex wave patterns. We employed an in vitro randomization and real-time imaging strategy to probe for the ability of cells to generate order from disorder. We found that, after randomization, PSM cells self-organized into several miniature emergent PSM structures (ePSM). Our results show an ordered macroscopic spatial arrangement of ePSM with evidence of an intrinsic length scale. Furthermore, cells actively synchronize oscillations in a Notch-signaling-dependent manner, re-establishing wave-like patterns of gene activity. We demonstrate that PSM cells self-organize by tuning oscillation dynamics in response to surrounding cells, leading to collective synchronization with an average frequency. These findings reveal emergent properties within an ensemble of coupled genetic oscillators.
Project description:In the last decade, several models with network adaptive mechanisms (link deletion-creation, dynamic synapses, dynamic gains) have been proposed as examples of self-organized criticality (SOC) to explain neuronal avalanches. However, all these systems present stochastic oscillations hovering around the critical region that are incompatible with standard SOC. Here we make a linear stability analysis of the mean field fixed points of two self-organized quasi-critical systems: a fully connected network of discrete time stochastic spiking neurons with firing rate adaptation produced by dynamic neuronal gains and an excitable cellular automata with depressing synapses. We find that the fixed point corresponds to a stable focus that loses stability at criticality. We argue that when this focus is close to become indifferent, demographic noise can elicit stochastic oscillations that frequently fall into the absorbing state. This mechanism interrupts the oscillations, producing both power law avalanches and dragon king events, which appear as bands of synchronized firings in raster plots. Our approach differs from standard SOC models in that it predicts the coexistence of these different types of neuronal activity.