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
Clàudia Payrató-Borràs et al 2024 J. Phys. Complex. 5 025013
Mutualistic relationships, where species interact to obtain mutual benefits, constitute an essential component of natural ecosystems. The use of ecological networks to represent the species and their ecological interactions allows the study of structural and dynamic patterns common to different ecosystems. However, by neglecting the temporal dimension of mutualistic communities, relevant insights into the organization and functioning of natural ecosystems can be lost. Therefore, it is crucial to incorporate empirical phenology -the cycles of species' activity within a season- to fully understand the impact of temporal variability on network architecture. In this paper, by using empirical datasets together with a set of synthetic models, we propose a framework to characterize the phenology of plant-pollinator communities and assess how it reshapes their portrayal as a network. Analyses of three empirical cases reveal that non-trivial information is missed when representing the network of interactions as static, which leads to overestimating the value of fundamental structural features. We discuss the implications of our findings for mutualistic relationships and intra-guild competition for common resources. We show that recorded interactions and species' activity duration are pivotal factors in accurately replicating observed patterns within mutualistic communities. Furthermore, our exploration of synthetic models underscores the system-specific character of the mechanisms driving phenology, increasing our understanding of the complexities of natural ecosystems.
Diogo L M Souza et al 2024 J. Phys. Complex. 5 025010
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 () 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 bistable states of wave patterns are obtained.
Matheus Henrique Junqueira Saldanha and Yoshito Hirata 2024 J. Phys. Complex. 5 025015
Seismicity is a complex phenomenon with a multitude of components involved. In order to perform forecasting, which has yet to be done sufficiently well, it is paramount to be in possession of information of all these components, and use this information effectively in a prediction model. In the literature, the influence of the Sun and the Moon in seismic activity on Earth has been discussed numerous times. In this paper we contribute to such discussion, giving continuity to a previous work. Most importantly, we instrument four earthquake catalogs from different regions, calculating the Moon tidal force at the region and time of each earthquake, which allows us to analyze the relation between the tidal forces and the earthquake magnitudes. At first, we find that the dynamical system governing Moon motion is unidirectionally coupled with seismic activity, indicating that the position of the Moon drives, to some extent, the earthquake generating process. Furthermore, we present an analysis that demonstrates a clear positive correlation between tidal force and earthquake magnitude. Finally, it is shown that the use of Moon tidal force data and sunspot number data can be used to improve next-day maximum magnitude forecasting, with the highest accuracy being achieved when using both kinds of data. We hope that our results encourage researchers to include data from Moon tidal forces and Sun activity in their earthquake forecasting models.
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.
Xinshan Jiao et al 2024 J. Phys. Complex. 5 025014
Link prediction aims to predict the potential existence of links between two unconnected nodes within a network based on the known topological characteristics. Evaluation metrics are used to assess the effectiveness of algorithms in link prediction. The discriminating ability of these evaluation metrics is vitally important for accurately evaluating link prediction algorithms. In this study, we propose an artificial network model, based on which one can adjust a single parameter to monotonically and continuously turn the prediction accuracy of the specifically designed link prediction algorithm. Building upon this foundation, we show a framework to depict the effectiveness of evaluating metrics by focusing on their discriminating ability. Specifically, a quantitative comparison in the abilities of correctly discerning varying prediction accuracies was conducted encompassing nine evaluation metrics: Precision, Recall, F1-Measure, Matthews correlation coefficient, balanced precision, the area under the receiver operating characteristic curve (AUC), the area under the precision-recall curve (AUPR), normalized discounted cumulative gain (NDCG), and the area under the magnified receiver operating characteristic. The results indicate that the discriminating abilities of the three metrics, AUC, AUPR, and NDCG, are significantly higher than those of other metrics.
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.
Paolo Bova et al 2024 J. Phys. Complex. 5 025009
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.
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.
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Ke Huang et al 2024 J. Phys. Complex. 5 025019
Futures trading in developing countries is now attracting more attention since investors may easily generate more excess return compared to the markets in developed countries, especially in Chinese market. In this paper, we analyzed the relationship between the centrality of commodity in the Chinese commodity futures market network and the optimal weight of each commodity in a portfolio, empirically examined the market systemic factors and commodity idiosyncratic factors that affect the centrality of commodity, and evaluated the effect of network structure on the optimization of commodity portfolio selection under the mean-variance framework. We found that the commodities with high network centrality are often related to industrial products with high volatility and small portfolio weights. We put forward a kind of commodity futures investment strategy based on this network and results showed that cumulative yield is better than other benchmark portfolios. The main contribution of this paper is to apply complex network theory to optimize futures portfolio selection by establishing the relationship between portfolio weight and commodity centrality in Chinese market, which is still under explored.
Thiago C Silva et al 2024 J. Phys. Complex. 5 025018
The post-World War II decades experienced rapid growth in international trade, but a trend of weakening globalization has been consolidating recently. We construct the international trade network (ITN) using bilateral trade (2010–2022) to assess how interconnectedness has evolved in the face of recent developments. Our analysis reveals that, while network connectivity initially improved, there has been a shift towards a negative trend since 2018, coinciding with an increasingly unfavorable environment for international trade. We also document significant changes in the roles of countries within the ITN. While the USA remains the primary hub and China solidifies its second position, key countries like Germany, France, Great Britain, and Japan have notably lost relevance, whereas nations like India and the Republic of Korea are gaining prominence. Finally, employing an econometric model, we show that countries with large economies, significant manufacturing sectors, lower inward foreign direct investment stock, and economic and geopolitical stability tend to occupy more central positions in the ITN.
Ilkka Kivimäki et al 2024 J. Phys. Complex. 5 025017
The randomized shortest paths (RSP) framework, developed for network analysis, extends traditional proximity and distance measures between two nodes, such as shortest path distance and commute cost distance (related to resistance distance). Consequently, the RSP framework has gained popularity in studies on landscape connectivity within ecology and conservation, where the behavior of animals is neither random nor optimal. In this work, we study how local perturbations in a network affect proximity and distance measures derived from the RSP framework. For this sensitivity analysis, we develop computable expressions for derivatives with respect to weights on the edges or nodes of the network. Interestingly, the sensitivity of expected cost to edge or node features provides a new signed network centrality measure, the negative covariance between edge/node visits and path cost, that can be used for pinpointing strong and weak parts of a network. It is also shown that this quantity can be interpreted as minus the endured expected detour (in terms of cost) when constraining the walk to pass through the node or the edge. Our demonstration of this framework focuses on a migration corridor for wild reindeer (Rangifer rangifer) in Southern Norway. By examining the sensitivity of the expected cost of movement between winter and calving ranges to perturbations in local areas, we have identified priority areas crucial for the conservation of this migration corridor. This innovative approach not only holds great promise for conservation and restoration of migration corridors, but also more generally for connectivity corridors between important areas for biodiversity (e.g. protected areas) and climate adaptation. Furthermore, the derivations and computational methods introduced in this work present fundamental features of the RSP framework. These contributions are expected to be of interest to practitioners applying the framework across various disciplines, ranging from ecology, transport and communication networks to machine learning.
Benjamin Krawciw et al 2024 J. Phys. Complex. 5 025016
Complex network theory has focused on properties of networks with real-valued edge weights. However, in signal transfer networks, such as those representing the transfer of light across an interferometer, complex-valued edge weights are needed to represent the manipulation of the signal in both magnitude and phase. These complex-valued edge weights introduce interference into the signal transfer, but it is unknown how such interference affects network properties such as small-worldness. To address this gap, we have introduced a small-world interferometer network model with complex-valued edge weights and generalized existing network measures to define the interferometric clustering coefficient, the apparent path length, and the interferometric small-world coefficient. Using high-performance computing resources, we generated a large set of small-world interferometers over a wide range of parameters in system size, nearest-neighbor count, and edge-weight phase and computed their interferometric network measures. We found that the interferometric small-world coefficient depends significantly on the amount of phase on complex-valued edge weights: for small edge-weight phases, constructive interference led to a higher interferometric small-world coefficient; while larger edge-weight phases induced destructive interference which led to a lower interferometric small-world coefficient. Thus, for the small-world interferometer model, interferometric measures are necessary to capture the effect of interference on signal transfer. This model is an example of the type of problem that necessitates interferometric measures, and applies to any wave-based network including quantum networks.
Matheus Henrique Junqueira Saldanha and Yoshito Hirata 2024 J. Phys. Complex. 5 025015
Seismicity is a complex phenomenon with a multitude of components involved. In order to perform forecasting, which has yet to be done sufficiently well, it is paramount to be in possession of information of all these components, and use this information effectively in a prediction model. In the literature, the influence of the Sun and the Moon in seismic activity on Earth has been discussed numerous times. In this paper we contribute to such discussion, giving continuity to a previous work. Most importantly, we instrument four earthquake catalogs from different regions, calculating the Moon tidal force at the region and time of each earthquake, which allows us to analyze the relation between the tidal forces and the earthquake magnitudes. At first, we find that the dynamical system governing Moon motion is unidirectionally coupled with seismic activity, indicating that the position of the Moon drives, to some extent, the earthquake generating process. Furthermore, we present an analysis that demonstrates a clear positive correlation between tidal force and earthquake magnitude. Finally, it is shown that the use of Moon tidal force data and sunspot number data can be used to improve next-day maximum magnitude forecasting, with the highest accuracy being achieved when using both kinds of data. We hope that our results encourage researchers to include data from Moon tidal forces and Sun activity in their earthquake forecasting models.
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.
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Harper et al
We combine momentum from machine learning with evolutionary dynamics, where momentum can be viewed as a simple mechanism of intergenerational memory similar to epigenetic mechanisms. Using information divergences as Lyapunov functions, we show that momentum accelerates the convergence of evolutionary dynamics including the continuous and discrete replicator equations and Euclidean gradient descent on populations. When evolutionarily stable states are present, these methods prove convergence for small learning rates or small momentum, and yield an analytic determination of the relative decrease in time to converge that agrees well with computations. The main results apply even when the evolutionary dynamic is not a gradient flow. We also show that momentum can alter the convergence properties of these dynamics, for example by breaking the cycling associated to the rock-paper-scissors landscape, leading to either convergence to the ordinarily non-absorbing equilibrium, or divergence, depending on the value and mechanism of momentum.
Carpineti et al
The investigation of the evolution of glaciers largely relies on the characterisation of extensive quantities like their mass, area, and perimeter. In this work we use fractal and multifractal analysis to investigate the non-extensive structural properties of the perimeters of glaciers in the Svalbard Archipelago. We show that the perimeters of the glaciers exhibit a fractal structure with a fractal dimension Df ≃ 1.25, independently from the area of the glaciers. The investigation of the multifractal properties of the perimeters shows that small glaciers exhibit a more pronounced multifractal structure, as witnessed by the larger range of generalized dimensions Dq needed to characterise them. The range ΔDq of generalised dimensions required to characterise the multifractal perimeter of a glacier exhibits a power-law dependence with exponent −1.2 from the area, and represents a non-extensive parameter able to grab effectively the dependence of the multifractal structure of the perimeters on the size of glaciers. The comparison with similar results obtained in a previous study performed on glaciers in the Lombardy region of the Italian Alps confirms the robustness of the analysis performed, which does not appear to be affected by the morphology of the substrate or by climate conditions.
Kobayashi et al
We computed the Lyapunov spectrum and finite-time Lyapunov exponents of a data-driven model
constructed using reservoir computing. This analysis was performed for two dynamics that exhibit a
highly dimensionally unstable structure. We focused on the reconstruction of heterochaotic dynam-
ics, which are characterized by the coexistence of different numbers of unstable dimensions. This
was achieved by computing fluctuations in the number of positive finite-time Lyapunov exponents.
Aguadé-Gorgorió et al
The possibility that some ecosystems can exist in alternative stable states has profound
implications for ecosystem conservation and restoration. Current ecological theory on
multistability mostly relies on few-species dynamical models, in which alternative states
are intrinsically related to specific non-linear dynamics. Recent theoretical advances,
however, have shown that multiple stable 'cliques' – small subsets of coexisting species–
can be present in species-rich models even under linear interactions. Yet, the mechanisms
governing the appearence and characteristics of these cliques remain largely unexplored.
In the present work, we investigate cliques in the generalized Lotka-Volterra model with
mathematical and computational techniques. Our findings reveal that simple probabilistic and dynamical constraints can explain the appearence, properties and stability
of cliques. Our work contributes to the understanding of alternative stable states in
complex ecological communities.
Laiq et al
As the number of IoT devices increases daily due to the rapid growth in technology, every device and network is vulnerable to attacks because it is exposed to the internet. Denial of Service (DoS) is a prevalent type of intrusion on the Internet of Things (IoT) network in which the server becomes down due to flooding requests. Distributed Denial of Service (DDoS) is a special type of DoS attack where the network of malicious computers called botnet consumes the target's system resources by flooding the requests. Edge computing is closely related to Industrial Internet of Things (IIoT), and industry 4.0. Both of them are relatively emerging technologies so security is a crucial part of them. By incorporating our contributions to the current and innovative dataset Edge-IIoT, the proposed study presents a novel approach to detect DDoS attacks in an IIoT network in the domain of edge computing, whether the traffic is normal or malicious (DDoS traffic). This study explores various Ensemble Learning (EL) techniques to predict normal and malicious DDoS traffic along with the type of DDoS attack. The study applies various preprocessing techniques like Synthetic Minority Over Sampling Technique (SMOTE), label encoding, etc. to enhance the model's performance and reveals how EL techniques performs better in terms of accuracy than the individual classifiers. Further, the performance of all EL techniques has been investigated in terms of all evaluation measures, including the elapsed time. This important addition not only broadens the focus of study in this area but also offers insightful comparisons of the efficiency and precision of various ensemble approaches as well as individual classifiers. The study achieved a maximum of 99.99% in all evaluation measures.