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
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.
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.
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.
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.
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.
Ruben Interian and Francisco A Rodrigues 2023 J. Phys. Complex. 4 035008
The erosion of social cohesion and polarization is one of the topmost societal risks. In this work, we investigated the evolution of polarization, influence, and domination in online interaction networks using a large Twitter dataset collected before and during the 2022 Brazilian elections. From a theoretical perspective, we develop a methodology called d-modularity that allows discovering the contribution of specific groups to network polarization using the well-known modularity measure. While the overall network modularity (somewhat unexpectedly) decreased, the proposed group-oriented approach reveals that the contribution of the right-leaning community to this modularity increased, remaining very high during the analyzed period. Our methodology is general enough to be used in any situation when the contribution of specific groups to overall network modularity and polarization is needed to investigate. Moreover, using the concept of partial domination, we are able to compare the reach of sets of influential profiles from different groups and their ability to accomplish coordinated communication inside their groups and across segments of the entire network. We show that in the whole network, the left-leaning high-influential information spreaders dominated, reaching a substantial fraction of users with fewer spreaders. However, when comparing domination inside the groups, the results are inverse. Right-leaning spreaders dominate their communities using few nodes, showing as the most capable of accomplishing coordinated communication. The results bring evidence of extreme isolation and the ease of accomplishing coordinated communication that characterized right-leaning communities during the 2022 Brazilian elections, which likely influenced the subsequent coup events in Brasilia.
Latest articles
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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.
Charlotte Lotze et al 2024 J. Phys. Complex. 5 025001
Ride sharing services combine trips of multiple users in the same vehicle and may provide more sustainable transport than private cars. As mobility demand varies during the day, the travel times experienced by passengers may substantially vary as well, making the service quality unreliable. We show through model simulations that such travel time fluctuations may be drastically reduced by stop pooling. Having users walk to meet at joint locations for pick-up or drop-off allows buses to travel more direct routes by avoiding frequent door-to-door detours, especially during high demand. We in particular propose adaptive stop pooling by adjusting the maximum walking distance to the temporally and spatially varying demand. The results highlight that adaptive stop pooling may substantially reduce travel time fluctuations while even improving the average travel time of ride sharing services, especially for high demand. Such quality improvements may in turn increase the acceptance and adoption of ride sharing services.
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.
Review articles
Open all abstracts, in this tab
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.
Accepted manuscripts
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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.
Zhang et al
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.
Takano et al
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.
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.
Roy et al
Performance modeling is a key issue in queuing theory and operation research. It is well-known that the length of a queue that awaits service or the time spent by a job in a queue depends not only on the service rate, but also crucially on the fluctuations in service time. The larger the fluctuations, the longer the delay becomes and hence, this is a major hindrance for the queue to operate efficiently. Various strategies have been adapted to prevent this drawback. In this perspective, we investigate the effects of one such novel strategy namely resetting or restart, an emerging concept in statistical physics and stochastic complex process, that was recently introduced to mitigate fluctuations-induced delays in queues. In particular, we show that a service resetting mechanism accompanied with an overhead time can remarkably shorten the average queue lengths and waiting times. We examine various resetting strategies and further shed light on the intricate role of the overhead times to the queuing performance. Our analysis opens up future avenues in operation research where resetting-based strategies can be universally promising.