The 2021 Nobel Prize in Physics recognized the fundamental role of complex systems in the natural sciences. In order to celebrate this milestone, this editorial presents the point of view of the editorial board of JPhys Complexity on the achievements, challenges, and future prospects of the field. To distinguish the voice and the opinion of each editor, this editorial consists of a series of editor perspectives and reflections on few selected themes. A comprehensive and multi-faceted view of the field of complexity science emerges. We hope and trust that this open discussion will be of inspiration for future research on complex systems.
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ISSN: 2632-072X
JPhys Complexity is a new, interdisciplinary and fully open access journal publishing the most exciting and significant developments across all areas of complex systems and networks.
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Ginestra Bianconi et al 2023 J. Phys. Complex. 4 010201
Viktor Jirsa and Hiba Sheheitli 2022 J. Phys. Complex. 3 015007
Neuroscience is home to concepts and theories with roots in a variety of domains including information theory, dynamical systems theory, and cognitive psychology. Not all of those can be coherently linked, some concepts are incommensurable, and domain-specific language poses an obstacle to integration. Still, conceptual integration is a form of understanding that provides intuition and consolidation, without which progress remains unguided. This paper is concerned with the integration of deterministic and stochastic processes within an information theoretic framework, linking information entropy and free energy to mechanisms of emergent dynamics and self-organization in brain networks. We identify basic properties of neuronal populations leading to an equivariant matrix in a network, in which complex behaviors can naturally be represented through structured flows on manifolds establishing the internal model relevant to theories of brain function. We propose a neural mechanism for the generation of internal models from symmetry breaking in the connectivity of brain networks. The emergent perspective illustrates how free energy can be linked to internal models and how they arise from the neural substrate.
Pavle Cajic et al 2024 J. Phys. Complex. 5 015021
The participation coefficient is a widely used metric of the diversity of a node's connections with respect to a modular partition of a network. An information-theoretic formulation of this concept of connection diversity, referred to here as participation entropy, has been introduced as the Shannon entropy of the distribution of module labels across a node's connected neighbors. While diversity metrics have been studied theoretically in other literatures, including to index species diversity in ecology, many of these results have not previously been applied to networks. Here we show that the participation coefficient is a first-order approximation to participation entropy and use the desirable additive properties of entropy to develop new metrics of connection diversity with respect to multiple labelings of nodes in a network, as joint and conditional participation entropies. The information-theoretic formalism developed here allows new and more subtle types of nodal connection patterns in complex networks to be studied.
Xue Gong et al 2024 J. Phys. Complex. 5 015022
Higher-order networks encode the many-body interactions existing in complex systems, such as the brain, protein complexes, and social interactions. Simplicial complexes are higher-order networks that allow a comprehensive investigation of the interplay between topology and dynamics. However, simplicial complexes have the limitation that they only capture undirected higher-order interactions while in real-world scenarios, often there is a need to introduce the direction of simplices, extending the popular notion of direction of edges. On graphs and networks the Magnetic Laplacian, a special case of connection Laplacian, is becoming a popular operator to address edge directionality. Here we tackle the challenge of handling directionality in simplicial complexes by formulating higher-order connection Laplacians taking into account the configurations induced by the simplices' directions. Specifically, we define all the connection Laplacians of directed simplicial complexes of dimension two and we discuss the induced higher-order diffusion dynamics by considering instructive synthetic examples of simplicial complexes. The proposed higher-order diffusion processes can be adopted in real scenarios when we want to consider higher-order diffusion displaying non-trivial frustration effects due to conflicting directionalities of the incident simplices.
Luca Mungo et al 2024 J. Phys. Complex. 5 012001
Network reconstruction is a well-developed sub-field of network science, but it has only recently been applied to production networks, where nodes are firms and edges represent customer-supplier relationships. We review the literature that has flourished to infer the topology of these networks by partial, aggregate, or indirect observation of the data. We discuss why this is an important endeavour, what needs to be reconstructed, what makes it different from other network reconstruction problems, and how different researchers have approached the problem. We conclude with a research agenda.
Lewis Higgins et al 2023 J. Phys. Complex. 4 025008
We study pitch control in football, using data from six complete seasons of the English Premier League. Our objective is to investigate features of pitch control in the data. We process the data to ensure consistency of the tracking and event datasets. This represents the largest coherent dataset analysed in the literature and allows the observation of consistent patterns across several seasons' data. We demonstrate that teams playing in front of a crowd at home control on average more of the pitch than teams playing away, which reduces to in matches played behind closed doors. We observe that match by match the difference in pitch control between the teams has a weak, positive correlation with the difference in expected goals (Pearson correlation R = 0.38). As a further manifestation of home advantage we find that in games which the two teams have equal pitch control, on average the home team accumulates greater expected goals (). The concept of weighted pitch control is introduced, by assigning a weight to regions of the pitch. We demonstrate that pitch control of the penalty box of the out-of-possession team is negatively correlated with expected goals in each of the six seasons, and interpret this apparently counter-intuitive result.
Tim Johnson and Nick Obradovich 2024 J. Phys. Complex. 5 015003
Will advanced artificial intelligence (AI) language models exhibit trust toward humans? Gauging an AI model's trust in humans is challenging because—absent costs for dishonesty—models might respond falsely about trusting humans. Accordingly, we devise a method for incentivizing machine decisions without altering an AI model's underlying algorithms or goal orientation and we employ the method in trust games between an AI model from OpenAI and a human experimenter (namely, author TJ). We find that the AI model exhibits behavior consistent with trust in humans at higher rates when facing actual incentives than when making hypothetical decisions—a finding that is robust to prompt phrasing and the method of game play. Furthermore, trust decisions appear unrelated to the magnitude of stakes and additional experiments indicate that they do not reflect a non-social preference for uncertainty.
Elisa Omodei et al 2022 J. Phys. Complex. 3 021001
In a rapidly changing world, facing an increasing number of socioeconomic, health and environmental crises, complexity science can help us to assess and quantify vulnerabilities, and to monitor and achieve the UN sustainable development goals. In this perspective, we provide three exemplary use cases where complexity science has shown its potential: poverty and socioeconomic inequalities, collective action for representative democracy, and computational epidemic modeling. We then review the challenges and limitations related to data, methods, capacity building, and, as a result, research operationalization. We finally conclude with some suggestions for future directions, urging the complex systems community to engage in applied and methodological research addressing the needs of the most vulnerable.
Samuel Johnson 2024 J. Phys. Complex. 5 01LT01
'Compartmental models' of epidemics are widely used to forecast the effects of communicable diseases such as COVID-19 and to guide policy. Although it has long been known that such processes take place on social networks, the assumption of 'random mixing' is usually made, which ignores network structure. However, 'super-spreading events' have been found to be power-law distributed, suggesting that the underlying networks may be scale free or at least highly heterogeneous. The random-mixing assumption would then produce an overestimation of the herd-immunity threshold for given R0; and a (more significant) overestimation of R0 itself. These two errors compound each other, and can lead to forecasts greatly overestimating the number of infections. Moreover, if networks are heterogeneous and change in time, multiple waves of infection can occur, which are not predicted by random mixing. A simple SIR model simulated on both Erdős–Rényi and scale-free networks shows that details of the network structure can be more important than the intrinsic transmissibility of a disease. It is therefore crucial to incorporate network information into standard models of epidemics.
Caterina A M La Porta and Stefano Zapperi 2023 J. Phys. Complex. 4 045004
Inequalities in wealth, income, access to food and healthcare have been rising worldwide in the past decades, approaching levels seen in the early 20th century. Here we study the relationships between wealth inequality and mobility for different segments of the population, comparing longitudinal surveys conducted in the USA and in Italy. The larger wealth inequality observed in the USA is reflected by poorer health conditions than in Italy. We also find that in both countries wealth mobility becomes slower at the two extremes of the wealth distribution. Households trapped in a state of persistent lack of wealth are generally experiencing greater food insecurity and poorer health than the general population. We interpret the observed association between inequality and immobility using a simple agent based model of wealth condensation driven by random returns and exchanges. The model describes well survey data on a qualitative level, but the mobility is generally overestimated by the model. We trace back this discrepancy to the way income is generated for low-wealth households which is not correctly accounted by the model. On the other hand, the model is excellent in describing the wealth dynamics within a restricted class of ultra-wealthy, as we demonstrate by analyzing billionaires lists. Our results suggest that different forms of inequality are intertwined and should therefore be addressed together.
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Masanori Takano et al 2024 J. Phys. Complex. 5 025005
The dynamics of coupled oscillators in a network are a significant topic in complex systems science. People with daily social rhythms interact through social networks in everyday life. This can be considered as a coupled oscillator in social networks, which is also true in online society (online social rhythms). Controlling online social rhythms can contribute to healthy daily rhythms and mental health. We consider controlling online social rhythms by introducing periodic forcing (pacemakers). However, theoretical studies predict that pacemaker effects do not spread widely across mutually connected networks such as social networks. We aimed to investigate the characteristics of the online social rhythms with pacemakers on an empirical online social network. Therefore, we conducted an intervention experiment on the online social rhythms of hundreds of players (participants who were pacemakers) using an avatar communication application (N = 416). We found that the intervention had little effect on neighbors' online social rhythms. This may be because mutual entrainment stabilizes the neighbors' and their friends' rhythms. That is, their online social rhythms were stable despite the disturbances. However, the intervention affected on neighbors' rhythms when a participant and their neighbor shared many friends. This suggests that interventions to densely connected player groups may make their and their friends' rhythms better. We discuss the utilization of these properties to improve healthy online social rhythms.
Jing Zhang et al 2024 J. Phys. Complex. 5 025006
Decision-making often overlooks the feedback between agents and the environment. Reinforcement learning is widely employed through exploratory experimentation to address problems related to states, actions, rewards, decision-making in various contexts. This work considers a new perspective, where individuals continually update their policies based on interactions with the spatial environment, aiming to maximize cumulative rewards and learn the optimal strategy. Specifically, we utilize the Q-learning algorithm to study the emergence of cooperation in a spatial population playing the donation game. Each individual has a Q-table that guides their decision-making in the game. Interestingly, we find that cooperation emerges within this introspective learning framework, and a smaller learning rate and higher discount factor make cooperation more likely to occur. Through the analysis of Q-table evolution, we disclose the underlying mechanism for cooperation, which may provide some insights to the emergence of cooperation in the real-world systems.
Mickaël D Chekroun et al 2024 J. Phys. Complex. 5 025004
Recent years have seen a surge in interest for leveraging neural networks to parameterize small-scale or fast processes in climate and turbulence models. In this short paper, we point out two fundamental issues in this endeavor. The first concerns the difficulties neural networks may experience in capturing rare events due to limitations in how data is sampled. The second arises from the inherent multiscale nature of these systems. They combine high-frequency components (like inertia-gravity waves) with slower, evolving processes (geostrophic motion). This multiscale nature creates a significant hurdle for neural network closures. To illustrate these challenges, we focus on the atmospheric 1980 Lorenz model, a simplified version of the Primitive Equations that drive climate models. This model serves as a compelling example because it captures the essence of these difficulties.
Massimiliano Fessina et al 2024 J. Phys. Complex. 5 025003
Tree-based machine learning algorithms provide the most precise assessment of the feasibility for a country to export a target product given its export basket. However, the high number of parameters involved prevents a straightforward interpretation of the results and, in turn, the explainability of policy indications. In this paper, we propose a procedure to statistically validate the importance of the products used in the feasibility assessment. In this way, we are able to identify which products, called explainers, significantly increase the probability to export a target product in the near future. The explainers naturally identify a low dimensional representation, the Feature Importance Product Space, that enhances the interpretability of the recommendations and provides out-of-sample forecasts of the export baskets of countries. Interestingly, we detect a positive correlation between the complexity of a product and the complexity of its explainers.
Yuan-Yuan Guo and Xiao-Pu Han 2024 J. Phys. Complex. 5 025002
In this article, we explore the concept and measurement of the degree of economic development pattern (DEDP) of economy, which refers to the extent to which the development of an economy can serve as a reference for other economies. Utilizing 76 macroeconomic indicators across 217 economies, the economic development paths in a standardized space of economy is compared to identify variations in DEDP through the regression analysis on the relationship between the similarity of development paths and the growth rate on gross domestic product (GDP) per capita. To measure DEDP of economy from different perspective, two types of metrics are constructed. One is the determination coefficient of regression analysis, which exhibits significant positive correlations with population size of economy, uncovering differences of development paths among economies of varying population sizes. The other type of metrics is based on the consistency on regression coefficients and effectively explains disparities among economies in the growth rate on GDP per capita, economic complexity index and economic fitness. These findings reveal the differences in development paths among different countries from the perspective of referentiality for development patterns, suggesting the potential existence of the paths with more universal meaning to economic development.
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Luca Mungo et al 2024 J. Phys. Complex. 5 012001
Network reconstruction is a well-developed sub-field of network science, but it has only recently been applied to production networks, where nodes are firms and edges represent customer-supplier relationships. We review the literature that has flourished to infer the topology of these networks by partial, aggregate, or indirect observation of the data. We discuss why this is an important endeavour, what needs to be reconstructed, what makes it different from other network reconstruction problems, and how different researchers have approached the problem. We conclude with a research agenda.
A Baptista et al 2023 J. Phys. Complex. 4 042001
Networks have provided extremely successful models of data and complex systems. Yet, as combinatorial objects, networks do not have in general intrinsic coordinates and do not typically lie in an ambient space. The process of assigning an embedding space to a network has attracted great interest in the past few decades, and has been efficiently applied to fundamental problems in network inference, such as link prediction, node classification, and community detection. In this review, we provide a user-friendly guide to the network embedding literature and current trends in this field which will allow the reader to navigate through the complex landscape of methods and approaches emerging from the vibrant research activity on these subjects.
Christopher S Dunham et al 2021 J. Phys. Complex. 2 042001
Numerous studies suggest critical dynamics may play a role in information processing and task performance in biological systems. However, studying critical dynamics in these systems can be challenging due to many confounding biological variables that limit access to the physical processes underpinning critical dynamics. Here we offer a perspective on the use of abiotic, neuromorphic nanowire networks as a means to investigate critical dynamics in complex adaptive systems. Neuromorphic nanowire networks are composed of metallic nanowires and possess metal-insulator-metal junctions. These networks self-assemble into a highly interconnected, variable-density structure and exhibit nonlinear electrical switching properties and information processing capabilities. We highlight key dynamical characteristics observed in neuromorphic nanowire networks, including persistent fluctuations in conductivity with power law distributions, hysteresis, chaotic attractor dynamics, and avalanche criticality. We posit that neuromorphic nanowire networks can function effectively as tunable abiotic physical systems for studying critical dynamics and leveraging criticality for computation.
Henrik Jeldtoft Jensen 2021 J. Phys. Complex. 2 032002
We present a brief review of power laws and correlation functions as measures of criticality and the relation between them. By comparing phenomenology from rain, brain and the forest fire model we discuss the relevant features of self-organisation to the vicinity about a critical state. We conclude that organisation to a region of extended correlations and approximate power laws may be behaviour of interest shared between the three considered systems.
Sindre W Haugland 2021 J. Phys. Complex. 2 032001
Chimera states, states of coexistence of synchronous and asynchronous motion, have been a subject of extensive research since they were first given a name in 2004. Increased interest has lead to their discovery in ever new settings, both theoretical and experimental. Less well-discussed is the fact that successive results have also broadened the notion of what actually constitutes a chimera state. In this article, we critically examine how the results for different model types and coupling schemes, as well as varying implicit interpretations of terms such as coexistence, synchrony and incoherence, have influenced the common understanding of what constitutes a chimera. We cover both theoretical and experimental systems, address various chimera-derived terms that have emerged over the years and finally reflect on the question of chimera states in real-world contexts.
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Souza et al
Spiral waves are spatial-temporal patterns that can emerge in different systems as heart tissues, chemical oscillators, ecological networks and the brain. These waves have been identified in the neocortex of turtles, rats, and humans, particularly during sleep-like states. Although their functions in cognitive activities remain until now poorly understood, these patterns are related to cortical activity modulation and contribute to cortical processing. In this work, we construct a neuronal network layer based on the spatial distribution of pyramidal neurons. Our main goal is to investigate how local connectivity and coupling strength are associated with the emergence of spiral waves. Therefore, we propose a trustworthy method capable of detecting different wave patterns, based on local and global phase order parameters. As a result, we find that the range of connection radius (R) plays a crucial role in the appearance of spiral waves. For R < 20 µm, only asynchronous activity is observed due to small number of connections. The coupling strength (gsyn ) greatly influences the pattern transitions for higher R, where spikes and bursts firing patterns can be observed in spiral and non-spiral waves. Finally, we show that for some values of R and gsyn bistable states of wave patterns are obtained.
Provata
When chaotic oscillators are coupled in complex networks a number of interesting synchronization phenomena emerge. Notable examples are the frequency and amplitude chimeras, chimera death states, solitary states as well as combinations of these. In a previous study [Journal of Physics: Complexity, 2020, 1(2), 025006], a toy model was introduced addressing possible mechanisms behind the formation of frequency chimera states. In the present study a variation of the toy model is proposed to address the formation of amplitude chimeras. The proposed oscillatory model is now equipped with an additional 3rd order equation modulating the amplitude of the network oscillators. This way, the single oscillators are constructed as bistable in amplitude and depending on the initial conditions their amplitude may result in one of the two stable fixed points. Numerical simulations demonstrate that when these oscillators are nonlocally coupled in networks, they organize in domains with alternating amplitudes (related to the two fixed points), naturally forming amplitude chimeras. A second extension of this model incorporates nonlinear terms merging amplitude together with frequency, and this extension allows for the spontaneous production of composite amplitude-and-frequency chimeras occurring simultaneously in the network. Moreover the extended model allows to understand the emergence of bump states via the continuous passage from chimera states, when both fixed point amplitudes are positive, to bump states when one of the two fixed points vanishes. The synchronization properties of the network are studied as a function of the system parameters for the case of amplitude chimeras, bump states and composite amplitude-and-frequency chimeras. The proposed mechanisms of creating domains with variable amplitudes and/or frequencies provide a generic scenario for understanding the formation of the complex synchronization phenomena observed in networks of coupled nonlinear and chaotic oscillators.
Bova et al
Auditors can play a vital role in ensuring that tech companies develop and deploy AI systems safely, taking into account not just immediate, but also systemic harms that may arise from the use of future AI capabilities. However, to support auditors in evaluating the capabilities and consequences of cutting-edge AI systems, governments may need to encourage a range of potential auditors to invest in new auditing tools and approaches. We use evolutionary game theory to model scenarios where the government wishes to incentivise auditing, but cannot discriminate between high and low-quality auditing. We warn that it is alarmingly easy to stumble on 'Adversarial incentives', which prevent a sustainable market for auditing AI systems from forming. Adversarial Incentives mainly reward auditors for catching unsafe behaviour. If AI companies learn to tailor their behaviour to the quality of audits, the lack of opportunities to catch unsafe behaviour will discourage auditors from innovating. Instead, we recommend that governments always reward auditors, except when they find evidence that those auditors failed to detect unsafe behaviour they should have. These 'Vigilant Incentives' could encourage auditors to find innovative ways to evaluate cutting-edge AI systems.
Overall, our analysis provides useful insights for the design and implementation of efficient incentive strategies for encouraging a robust auditing ecosystem.
Vasellini et al
We introduce an Agent Based Model (ABM) framework to investigate how an alternative to classic image score and gossip can support the emergence of cooperation in a Repeated Prisoner Dilemma Game (RPDG) with agents employing mixed strategies. We debate the universality of image scores, arguing that they cannot be considered an objective property of the agents observed but rather a subjective property of each observer. From this assumption, we develop a private list mechanism for opponent selection and gossip sharing among the population of the simulation. The results show that the private list mechanism is able to foster the emergence of cooperation, and that for various levels of list usage different levels of cooperation correspond in the system. Finally, we observe interesting topological properties emerging, with networks characterised by one "super-hub" connected to every other node, suggesting the emergence of centralized entities to support cooperation. and that for various level of list usage different levels of cooperation correspond in the system. Finally, we observed interesting topological properties emerging, with networks characterised by one "super-hub" connected to every other node, suggesting the emergence of centralized entities to support cooperation.
Lane et al
This study presents a data-driven framework for modeling complex systems, with a specific emphasis on traffic modeling. 
Traditional methods in traffic modeling often rely on assumptions regarding vehicle interactions. 
Our approach comprises two steps: first, utilizing information-theoretic (IT) tools to identify interaction directions and candidate variables thus eliminating assumptions, and second, employing the Sparse Identification of Nonlinear Systems (SINDy) tool to establish functional relationships. 
We validate the framework's efficacy using synthetic data from two distinct traffic models, while considering measurement noise. 
Results show that IT tools can reliably detect directions of interaction as well as instances of no interaction.
SINDy proves instrumental in creating precise functional relationships and determining coefficients in tested models. 
The innovation of our framework lies in its ability to use data-driven approach to model traffic dynamics without relying on assumptions, thus offering applications in various complex systems beyond traffic.