Individual heterogeneity generating explosive system network dynamics

Evolutionary dynamics in financial markets with heterogeneities in investment strategies and reference points

In nature and human societies, the effects of homogeneous and heterogeneous characteristics on the evolution of collective behaviors are quite different from each other. By incorporating pair pattern strategies and reference point strategies into an agent-based model, we have investigated the effects of homogeneous and heterogeneous investment strategies and reference points on price movement. In the market flooded with the investors with homogeneous investment strategies or homogeneous reference points, large price fluctuations occur. In the market flooded with the investors with heterogeneous investment strategies or heterogeneous reference points, moderate price fluctuations occur. The coexistence of different kinds of investment strategies can not only refrain from the occurrence of large price fluctuations but also the occurrence of no-trading states. The present model reveals that the coexistence of heterogeneous populations, whether they are the individuals with heterogeneous investment strategies or heterogeneous reference points of stock prices, is an important factor for the stability of the stock market.

Shockwavelike Behavior across Social Media

Online communities featuring "anti-X" hate and extremism, somehow thrive online despite moderator pressure. We present a first-principles theory of their dynamics, which accounts for the fact that the online population comprises diverse individuals and evolves in time. The resulting equation represents a novel generalization of nonlinear fluid physics and explains the observed behavior across scales. Its shockwavelike solutions explain how, why, and when such activity rises from "out-of-nowhere," and show how it can be delayed, reshaped, and even prevented by adjusting the online collective chemistry. This theory and findings should also be applicable to anti-X activity in next-generation ecosystems featuring blockchain platforms and Metaverses.

Emergence of Polarization in Coevolving Networks

Polarization is a ubiquitous phenomenon in social systems. Empirical studies document substantial evidence for opinion polarization across social media, showing a typical bipolarized pattern devising individuals into two groups with opposite opinions. While coevolving network models have been proposed to understand polarization, existing works cannot generate a stable bipolarized structure. Moreover, a quantitative and comprehensive theoretical framework capturing generic mechanisms governing polarization remains unaddressed. In this Letter, we discover a universal scaling law for opinion distributions, characterized by a set of scaling exponents. These exponents classify social systems into bipolarized and depolarized phases. We find two generic mechanisms governing the polarization dynamics and propose a coevolving framework that counts for opinion dynamics and network evolution simultaneously. Under a few generic assumptions on social interactions, we find a stable bipolarized community structure emerges naturally from the coevolving dynamics. Our theory analytically predicts two-phase transitions across three different polarization phases in line with the empirical observations for the Facebook and blogosphere data sets. Our theory not only accounts for the empirically observed scaling laws but also allows us to predict scaling exponents quantitatively.

Effect of load-capacity heterogeneity on cascading overloads in networks

Heterogeneity in the load capacity of nodes is a common characteristic of many real-world networks that can dramatically affect their robustness to cascading overloads. However, most studies seeking to model cascading failures have ignored variations in nodal load capacity and functionality. The present study addresses this issue by extending the local load redistribution model to include heterogeneity in nodal load capacity and heterogeneity in the types of nodes employed in the network configuration and exploring how these variations affect network robustness. Theoretical and numerical analyses demonstrate that the extent of cascading failure is influenced by heterogeneity in nodal load capacity, while it is relatively insensitive to heterogeneity in nodal configuration. Moreover, the probability of cascading failure initiation at the critical state increases as the range of nodal load capacities increases. However, for large-scale networks with degree heterogeneity, a wide range of nodal load capacities can also suppress the spread of failure after its initiation. In addition, the analysis demonstrates that heterogeneity in nodal load capacity increases and decreases the extent of cascading failures in networks with sublinear and superlinear load distributions, respectively. These findings may provide some practical implications for controlling the spread of cascading failure.

Random heterogeneity outperforms design in network synchronization

A widely held assumption on network dynamics is that similar components are more likely to exhibit similar behavior than dissimilar ones and that generic differences among them are necessarily detrimental to synchronization. Here, we show that this assumption does not generally hold in oscillator networks when communication delays are present. We demonstrate, in particular, that random parameter heterogeneity among oscillators can consistently rescue the system from losing synchrony. This finding is supported by electrochemical-oscillator experiments performed on a multielectrode array network. Remarkably, at intermediate levels of heterogeneity, random mismatches are more effective in promoting synchronization than parameter assignments specifically designed to facilitate identical synchronization. Our results suggest that, rather than being eliminated or ignored, intrinsic disorder in technological and biological systems can be harnessed to help maintain coherence required for function.

Emergent dynamics of extremes in a population driven by common information sources and new social media algorithms

We quantify how and when extreme subpopulations emerge in a model society despite everyone having the same information and available resources – and show that counterintuitively these extremes will likely be enhanced over time by new social media algorithms designed to reduce division. We verify our analysis mathematically, and show it reproduces (a) the time-dependent behavior observed in controlled experiments on humans, (b) the findings of a recent study of online behavior by Facebook concerning the impact of ‘soft’ and ‘hard’ news, (c) the observed temporal emergence of extremes in U.S. House of Representatives voting, and (d) the real-time emergence of a division in national opinion during the ongoing peace process in Colombia. We uncover a novel societal tipping point which is a ‘ghost’ of a nearby saddle-node bifurcation from dynamical systems theory, and which provides a novel policy opportunity for preventing extremes from emerging.

The Heterogeneity Problem: Approaches to Identify Psychiatric Subtypes

The imprecise nature of psychiatric nosology restricts progress towards characterizing and treating mental health disorders. One issue is the 'heterogeneity problem': different causal mechanisms may relate to the same disorder, and multiple outcomes of interest can occur within one individual. Our review tackles this heterogeneity problem, providing considerations, concepts, and approaches for investigators examining human cognition and mental health. We highlight the difficulty of pure dimensional approaches due to 'the curse of dimensionality'. Computationally, we consider supervised and unsupervised statistical approaches to identify putative subtypes within a population. However, we emphasize that subtype identification should be linked to a particular outcome or question. We conclude with novel hybrid approaches that can identify subtypes tied to outcomes, and may help advance precision diagnostic and treatment tools.