1. Adaptive rumor propagation and activity contagion in higher-order networksYafang Dong, Liang'an Huo, Matjaž Perc, Stefano Boccaletti, 2025, original scientific article Abstract: Rumors in social systems are omnipresent. While traditional models focus on pairwise interactions, the collective effects of group interactions are insufficiently explored. Here we present a rumor propagation model on higher-order networks that incorporates 2-simplex structures and adaptive transitions between active and passive individuals. We find that higher-order networks substantially lower the propagation threshold and intensify nonlinear spreading effects. Active individuals are key drivers of rumor propagation and persistence. With active contagion, we observe that higher-order propagation increases peak and steady-state densities of active spreaders, thus extending the propagation and lifespan of rumors. We also apply a sequential quadratic programming algorithm to optimize the parameters of our model and validate its accuracy and applicability on real-world data. These results advance our understanding of contagion in higher-order social networks and support the design of targeted strategies for rumor mitigation. Keywords: rumor propagation, activity contagion, higher-order networks, social physics Published in DKUM: 24.06.2025; Views: 0; Downloads: 0
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2. Structural roles and gender disparities in corruption networksArthur A. B. Pessa, Alvaro F. Martins, Mônica V. Prates, Sebastián Gonçalves, Cristina Masoller, Matjaž Perc, Haroldo V. Ribeiro, 2025, original scientific article Abstract: Criminal activities are predominantly due to males, with females exhibiting a significantly lower involvement, especially in serious offenses. This pattern extends to organized crime, where females are often perceived as less tolerant to illegal practices. However, the roles of males and females within corruption networks are less understood. Here, we analyze data from political scandals in Brazil and Spain to shed light on gender differences in corruption networks. Our findings reveal that females constitute 10% and 20% of all agents in the Brazilian and Spanish corruption networks, respectively, with these proportions remaining stable over time and across different scandal sizes. Despite this disparity in representation, centrality measures are comparable between genders, except among highly central individuals, for which males are further overrepresented. Additionally, gender has no significant impact on network resilience, whether through random dismantling or targeted attacks on the largest component. Males are more likely to be involved in multiple scandals than females, and scandals predominantly involving females are rare, though these differences are explained by a null network model in which gender is randomly assigned while maintaining gender proportions. Our results further reveal that the underrepresentation of females partially explains gender homophily in network associations, although in the Spanish network, male-to-male connections exceed expectations derived from a null model. Keywords: gender disparity, corruption network, political scandal, social physics, social physics Published in DKUM: 25.04.2025; Views: 0; Downloads: 0
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3. Two-by-two ordinal patterns in art paintingsMateus M. Tarozo, Arthur A. B. Pessa, Luciano Zunino, Osvaldo A. Rosso, Matjaž Perc, Haroldo V. Ribeiro, 2025, original scientific article Abstract: Quantitative analysis of visual arts has recently expanded to encompass a more extensive array of artworks due to the availability of large-scale digitized art collections. Consistent with formal analyses by art historians, many of these studies highlight the significance of encoding spatial structures within artworks to enhance our understanding of visual arts. However, defining universally applicable, interpretable, and sufficiently simple units that capture the essence of paintings and their artistic styles remains challenging. Here, we examine ordering patterns in pixel intensities within two-by-two partitions of images from nearly 140,000 paintings created over the past 1,000 years. These patterns, categorized into 11 types based on arguments of continuity and symmetry, are both universally applicable and detailed enough to correlate with low-level visual features of paintings. We uncover a universal distribution of these patterns, with consistent prevalence within groups, yet modulated across groups by a nontrivial interplay between pattern smoothness and the likelihood of identical pixel intensities. This finding provides a standardized metric for comparing paintings and styles, further establishing a scale to measure deviations from the average prevalence. Our research also shows that these simple patterns carry valuable information for identifying painting styles, though styles generally exhibit considerable variability in the prevalence of ordinal patterns. Moreover, shifts in the prevalence of these patterns reveal a trend in which artworks increasingly diverge from the average incidence over time; however, this evolution is neither smooth nor uniform, with substantial variability in pattern prevalence, particularly after the 1930s. Keywords: spatial patterns, complexity, esthetic measure, art history, social physics Published in DKUM: 01.04.2025; Views: 0; Downloads: 3
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4. Local and global stimuli in reinforcement learningDanyang Jia, Hao Guo, Zhao Song, Lei Shi, Xinyang Deng, Matjaž Perc, Zhen Wang, 2021, original scientific article Abstract: In efforts to resolve social dilemmas, reinforcement learning is an alternative to imitation and exploration in evolutionary game theory. While imitation and exploration rely on the performance of neighbors, in reinforcement learning individuals alter their strategies based on their own performance in the past. For example, according to the Bush-Mosteller model of reinforcement learning, an individual's strategy choice is driven by whether the received payoff satisfies a preset aspiration or not. Stimuli also play a key role in reinforcement learning in that they can determine whether a strategy should be kept or not. Here we use the Monte Carlo method to study pattern formation and phase transitions towards cooperation in social dilemmas that are driven by reinforcement learning. We distinguish local and global players according to the source of the stimulus they experience. While global players receive their stimuli from the whole neighborhood, local players focus solely on individual performance. We show that global players play a decisive role in ensuring cooperation, while local players fail in this regard, although both types of players show properties of "moody cooperators". In particular, global players evoke stronger conditional cooperation in their neighborhoods based on direct reciprocity, which is rooted in the emerging spatial patterns and stronger interfaces around cooperative clusters. Keywords: evolutionary game theory, cooperation, learning, social physics Published in DKUM: 03.03.2025; Views: 0; Downloads: 1
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5. The self-organizing impact of averaged payoffs on the evolution of cooperationAttila Szolnoki, Matjaž Perc, 2021, original scientific article Abstract: According to the fundamental principle of evolutionary game theory, the more successful strategy in a population should spread. Hence, during a strategy imitation process a player compares its payoff value to the payoff value held by a competing strategy. But this information is not always accurate. To avoid ambiguity a learner may therefore decide to collect a more reliable statistics by averaging the payoff values of its opponents in the neighborhood, and makes a decision afterwards. This simple alteration of the standard microscopic protocol significantly improves the cooperation level in a population. Furthermore, the positive impact can be strengthened by increasing the role of the environment and the size of the evaluation circle. The mechanism that explains this improvement is based on a self-organizing process which reveals the detrimental consequence of defector aggregation that remains partly hidden during face-to-face comparisons. Notably, the reported phenomenon is not limited to lattice populations but remains valid also for systems described by irregular interaction networks. Keywords: evolutionary game theory, cooperation, learning, social physics Published in DKUM: 03.03.2025; Views: 0; Downloads: 2
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6. Optimal governance and implementation of vaccination programmes to contain the COVID-19 pandemicMahendra Piraveenan, Shailendra Sawleshwarkar, Michael Walsh, Iryna Zablotska, Samit Bhattacharyya, Habib Hassan Farooqui, Tarun Bhatnagar, Anup Karan, Manoj Murhekar, Sanjay P. Zodpey, K. S. Mallikarjuna Rao, Philippa Pattison, Albert Y. Zomaya, Matjaž Perc, 2021, original scientific article Abstract: Since the recent introduction of several viable vaccines for SARS-CoV-2, vaccination uptake has become the key factor that will determine our success in containing the COVID-19 pandemic. We argue that game theory and social network models should be used to guide decisions pertaining to vaccination programmes for the best possible results. In the months following the introduction of vaccines, their availability and the human resources needed to run the vaccination programmes have been scarce in many countries. Vaccine hesitancy is also being encountered from some sections of the general public. We emphasize that decision-making under uncertainty and imperfect information, and with only conditionally optimal outcomes, is a unique forte of established game-theoretic modelling. Therefore, we can use this approach to obtain the best framework for modelling and simulating vaccination prioritization and uptake that will be readily available to inform important policy decisions for the optimal control of the COVID-19 pandemic. Keywords: COVID-19, evolutionary game theory, digital epidemiology, vaccination, social network, public goods game, social physics Published in DKUM: 28.02.2025; Views: 0; Downloads: 3
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7. Seasonal payoff variations and the evolution of cooperation in social dilemmasAttila Szolnoki, Matjaž Perc, 2019, original scientific article Abstract: Varying environmental conditions affect relations between interacting individuals in social dilemmas, thus affecting also the evolution of cooperation. Oftentimes these environmental variations are seasonal and can therefore be mathematically described as periodic changes. Accordingly, we here study how periodic shifts between different manifestations of social dilemmas affect cooperation. We observe a non-trivial interplay between the inherent spatiotemporal dynamics that characterizes the spreading of cooperation in a particular social dilemma type and the frequency of payoff changes. In particular, we show that periodic changes between two available games with global ordering best be fast, while periodic changes between global and local ordering games best be slow for cooperation to thrive. We also show that the frequency of periodic changes between two local ordering social dilemmas is irrelevant, because then the process is fast and simply the average cooperation level of the two is returned. The structure of the interaction network plays an important role too in that lattices promote local ordering, whilst random graphs hinder the formation of compact cooperative clusters. Conversely, for local ordering the regular structure of the interaction network is only marginally relevant as role-separating checkerboard patterns do not rely on long-range order. Keywords: cooperation, social dilemma, social physics, phase transition, mixed games Published in DKUM: 26.02.2025; Views: 0; Downloads: 2
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8. Clustering patterns in efficiency and the coming-of-age of the cryptocurrency marketHigor Y. D. Sigaki, Matjaž Perc, Haroldo V. Ribeiro, 2019, original scientific article Abstract: The efficient market hypothesis has far-reaching implications for financial trading and market stability. Whether or not cryptocurrencies are informationally efficient has therefore been the subject of intense recent investigation. Here, we use permutation entropy and statistical complexity over sliding time-windows of price log returns to quantify the dynamic efficiency of more than four hundred cryptocurrencies. We consider that a cryptocurrency is efficient within a time-window when these two complexity measures are statistically indistinguishable from their values obtained on randomly shuffled data. We find that 37% of the cryptocurrencies in our study stay efficient over 80% of the time, whereas 20% are informationally efficient in less than 20% of the time. Our results also show that the efficiency is not correlated with the market capitalization of the cryptocurrencies. A dynamic analysis of informational efficiency over time reveals clustering patterns in which different cryptocurrencies with similar temporal patterns form four clusters, and moreover, younger currencies in each group appear poised to follow the trend of their 'elders'. The cryptocurrency market thus already shows notable adherence to the efficient market hypothesis, although data also reveals that the coming-of-age of digital currencies is in this regard still very much underway. Keywords: cryptocurrency, market efficiency, financial trading, social physics Published in DKUM: 26.02.2025; Views: 0; Downloads: 2
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9. Evolutionary dynamics of any multiplayer game on regular graphsChaoqian Wang, Matjaž Perc, Attila Szolnoki, 2024, original scientific article Abstract: Multiplayer games on graphs are at the heart of theoretical descriptions of key evolutionary processes that govern vital social and natural systems. However, a comprehensive theoretical framework for solving multiplayer games with an arbitrary number of strategies on graphs is still missing. Here, we solve this by drawing an analogy with the Balls-and-Boxes problem, based on which we show that the local configuration of multiplayer games on graphs is equivalent to distributing k identical co-players among n distinct strategies. We use this to derive the replicator equation for any n-strategy multiplayer game under weak selection, which can be solved in polynomial time. As an example, we revisit the second-order free-riding problem, where costly punishment cannot truly resolve social dilemmas in a well-mixed population. Yet, in structured populations, we derive an accurate threshold for the punishment strength, beyond which punishment can either lead to the extinction of defection or transform
the system into a rock-paper-scissors-like cycle. The analytical solution also qualitatively agrees with the phase diagrams that were previously obtained for non-marginal selection strengths. Our framework thus allows an exploration of any multi-strategy multiplayer game on regular graphs. Keywords: evolutionary game theory, cooperation, network, social physics Published in DKUM: 26.02.2025; Views: 0; Downloads: 7
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10. Collective dynamics of stock market effciencyLuiz G. A. Alves, Higor Y. D. Sigaki, Matjaž Perc, Haroldo V. Ribeiro, 2020, original scientific article Abstract: Summarized by the efcient market hypothesis, the idea that stock prices fully refect all available information is always confronted with the behavior of real-world markets. While there is plenty of evidence indicating and quantifying the efciency of stock markets, most studies assume this efciency to be constant over time so that its dynamical and collective aspects remain poorly understood. Here we defne the time-varying efciency of stock markets by calculating the permutation entropy within sliding time-windows of log-returns of stock market indices. We show that major world stock markets can be hierarchically classifed into several groups that display similar long-term efciency profles. However, we also show that efciency ranks and clusters of markets with similar trends are only stable for a few months at a time. We thus propose a network representation of stock markets that aggregates their short-term efciency patterns into a global and coherent picture. We fnd this fnancial network to be strongly entangled while also having a modular structure that consists of two distinct groups of stock markets. Our results suggest that stock market efciency is a collective phenomenon that can drive its operation at a high level of informational efciency, but also places the entire system under risk of failure. Keywords: collective dynamics, social physics, econophysics, stock market Published in DKUM: 14.01.2025; Views: 0; Downloads: 4
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