Optimizing parameter search for community detection in time-evolving networks of complex systems.

Network representations have been effectively employed to analyze complex systems across various areas and applications, leading to the development of network science as a core tool to study systems with multiple components and complex interactions. There is a growing interest in understanding the temporal dynamics of complex networks to decode the underlying dynamic processes through the temporal changes in network structures. Community detection algorithms, which are specialized clustering algorithms, have been instrumental in studying these temporal changes. They work by grouping nodes into communities based on the structure and intensity of network connections over time, aiming to maximize the modularity of the network partition. However, the performance of these algorithms is highly influenced by the selection of resolution parameters of the modularity function used, which dictate the scale of the represented network, in both size of communities and the temporal resolution of the dynamic structure. The selection of these parameters has often been subjective and reliant on the characteristics of the data used to create the network. Here, we introduce a method to objectively determine the values of the resolution parameters based on the elements of self-organization and scale-invariance. We propose two key approaches: (1) minimization of biases in spatial scale network characterization and (2) maximization of scale-freeness in temporal network reconfigurations. We demonstrate the effectiveness of these approaches using benchmark network structures as well as real-world datasets. To implement our method, we also provide an automated parameter selection software package that can be applied to a wide range of complex systems.

Intermittent brain network reconfigurations and the resistance to social media influence.

Since its development, social media has grown as a source of information and has a significant impact on opinion formation. Individuals interact with others and content via social media platforms in a variety of ways, but it remains unclear how decision-making and associated neural processes are impacted by the online sharing of informational content, from factual to fabricated. Here, we use EEG to estimate dynamic reconfigurations of brain networks and probe the neural changes underlying opinion change (or formation) within individuals interacting with a simulated social media platform. Our findings indicate that the individuals who changed their opinions are characterized by less frequent network reconfigurations while those who did not change their opinions tend to have more flexible brain networks with frequent reconfigurations. The nature of these frequent network configurations suggests a fundamentally different thought process between intervals in which individuals are easily influenced by social media and those in which they are not. We also show that these reconfigurations are distinct to the brain dynamics during an in-person discussion with strangers on the same content. Together, these findings suggest that brain network reconfigurations may not only be diagnostic to the informational context but also the underlying opinion formation.

Self-organized spiral patterns at the edge of an order-disorder nonequilibrium phase transition.

We present a spatially extended version of the Wood-Van den Broeck-Kawai-Lindenberg stochastic phase-coupled oscillator model. Our model is embedded in two-dimensional (2d) array with a range-dependent interaction. The Wood-Van den Broeck-Kawai-Lindenberg model is known to present a phase transition from a disordered state to a globally oscillatory phase in which the majority of the units are in the same discrete phase. Here we address a parameter combination in which such global oscillations are not present. We explore the role of the interaction range from a nearest neighbor coupling in which a disordered phase is observed and the global coupling in which the population concentrate in a single phase. We find that for intermediate interaction range the system presents spiral wave patterns that are strongly influenced by the initial conditions and can spontaneously emerge from the stochastic nature of the model. Our results present a spatial oscillatory pattern not observed previously in the Wood-Van den Broeck-Kawai-Lindenberg model and are corroborated by a spatially extended mean-field calculation.

Oscillations and collective excitability in a model of stochastic neurons under excitatory and inhibitory coupling.

We study a model with excitable neurons modeled as stochastic units with three states, representing quiescence, firing, and refractoriness. The transition rates between quiescence and firing depend exponentially on the number of firing neighbors, whereas all other rates are kept constant. This model class was shown to exhibit collective oscillations (synchronization) if neurons are spiking autonomously, but not if neurons are in the excitable regime. In both cases, neurons were restricted to interact through excitatory coupling. Here we show that a plethora of collective phenomena appear if inhibitory coupling is added. Besides the usual transition between an absorbing and an active phase, the model with excitatory and inhibitory neurons can also undergo reentrant transitions to an oscillatory phase. In the mean-field description, oscillations can emerge through supercritical or subcritical Hopf bifurcations, as well as through infinite period bifurcations. The model has bistability between active and oscillating behavior, as well as collective excitability, a regime where the system can display a peak of global activity when subject to a sufficiently strong perturbation. We employ a variant of the Shinomoto-Kuramoto order parameter to characterize the phase transitions and their system-size dependence.