Physics

Models of complex networks often incorporate node-intrinsic properties abstracted as hidden variables. The probability of connections in the network is then a function of these variables. Real-world networks evolve over time, and many exhibit dynamics of node characteristics as well as of linking structure. Here we introduce and study natural temporal extensions of static hidden-variable network models with stochastic dynamics of hidden variables and links. The rates of the hidden variable dynamics and link dynamics are controlled by two parameters, and snapshots of networks in the dynamic models may or may not be equivalent to a static model, depending on the location in the parameter phase diagram. We quantify deviations from static-like behavior, and examine the level of structural persistence in the considered models. We explore temporal versions of popular static models with community structure, latent geometry, and degree-heterogeneity. We do not attempt to directly model real networks, but comment on interesting qualitative resemblances, discussing possible extensions, generalizations, and applications.

Prisoner's dilemma game is the most commonly used model of spatial evolutionary game which is considered as a paradigm to portray competition among selfish individuals. In recent years, Win-Stay-Lose-Learn, a strategy updating rule base on aspiration, has been proved to be an effective model to promote cooperation in spatial prisoner's dilemma game, which leads aspiration to receive lots of attention. But in many research the assumption that individual's aspiration is fixed is inconsistent with recent results from psychology. In this paper, according to Expected Value Theory and Achievement Motivation Theory, we propose a dynamic aspiration model based on Win-Stay-Lose-Learn rule in which individual's aspiration is inspired by its payoff. It is found that dynamic aspiration has a significant impact on the evolution process, and different initial aspirations lead to different results, which are called Stable Coexistence under Low Aspiration, Dependent Coexistence under Moderate aspiration and Defection Explosion under High Aspiration respectively. Furthermore, a deep analysis is performed on the local structures which cause cooperator's existence or defector's expansion, and the evolution process for different parameters including strategy and aspiration. As a result, the intrinsic structures leading to defectors' expansion and cooperators' survival are achieved for different evolution process, which provides a penetrating understanding of the evolution. Compared to fixed aspiration model, dynamic aspiration introduces a more satisfactory explanation on population evolution laws and can promote deeper comprehension for the principle of prisoner's dilemma.

We study the evolution of two mutually interacting games with both pairwise games as well as the public goods game on different topologies. On 2d square lattices, we reveal that the game-game interaction can promote the cooperation prevalence in all cases, and the cooperation-defection phase transitions even become absent and fairly high cooperation is expected when the interaction goes to be very strong. A mean-field theory is developed that points out new dynamical routes arising therein. Detailed analysis shows indeed that there are rich categories of interactions in either individual or bulk scenario: invasion, neutral, and catalyzed types; their combination puts cooperators at a persistent advantage position, which boosts the cooperation. The robustness of the revealed reciprocity is strengthened by the studies of model variants, including asymmetrical or time-varying interactions, games of different types, games with time-scale separation, different updating rules etc. The structural complexities of the underlying population, such as Newman--Watts small world networks, Erd?s--Rényi random networks, and Barabási--Albert networks, also do not alter the working of the dynamical reciprocity. In particular, as the number of games engaged increases, the cooperation level continuously improves in general. Our work thus uncovers a new class of cooperation mechanism and indicates the great potential for human cooperation where concurrent issues are so often seen in the real world.

A broad range of dynamical systems involve multi-body interactions, or group interactions, which may not be encoded in traditional graphical structures. In this work, we focus on a canonical example from opinion dynamics, the Majority Rule, and investigate the possibility to represent and analyse the system by means of hypergraphs. We explore the formation of consensus and restrict our attention to interaction groups of size 3 , in order to simplify our analysis from a combinatorial perspective. We propose different types of hypergraph models, incorporating modular structure or degree heterogeneity, and recast the dynamics in terms of Fokker-Planck equations, which allows us to predict the transient dynamics toward consensus. Numerical simulations show a very good agreement between the stochastic dynamics and theoretical predictions for large population sizes.

Burstiness, the tendency of interaction events to be heterogeneously distributed in time, is critical to information diffusion in physical and social systems. However, an analytical framework capturing the effect of burstiness on generic dynamics is lacking. We develop a master equation formalism to study cascades on temporal networks with burstiness modelled by renewal processes. Supported by numerical and data-driven simulations, we describe the interplay between heterogeneous temporal interactions and models of threshold-driven and epidemic spreading. We find that increasing interevent time variance can both accelerate and decelerate spreading for threshold models, but can only decelerate epidemic spreading. When accounting for the skewness of different interevent time distributions, spreading times collapse onto a universal curve. Our framework uncovers a deep yet subtle connection between generic diffusion mechanisms and underlying temporal network structures that impacts on a broad class of networked phenomena, from spin interactions to epidemic contagion and language dynamics.

The global SARS-CoV-2 pandemic suggests a novel type of disease spread dynamics. WHO states that there is currently no evidence that people who have recovered from COVID-19 and have antibodies are immune from a second infection [WHO]. Conventional mathematical models consider cases for which a recovered individual either becomes susceptible again or develops an immunity. Here, we study the case where infected agents recover and only develop immunity if they are continuously infected for some time. Otherwise, they become susceptible again. We show that field theory bounds the peak of the infectious rate. Consequently, the theory's phases characterise the disease dynamics: (i) a pandemic phase and (ii) a response regime. The model excellently describes the epidemic spread of the SARS-CoV-2 outbreak in the city of Wuhan, China. We find that only 30% of the recovered agents have developed an immunity. We anticipate our paper to influence the decision making upon balancing the economic impact and the pandemic impact on society. As long as disease controlling measures keep the disease dynamics in the "response regime", a pandemic escalation ('second wave') is ruled out.

We apply the cavity master equation (CME) approach to epidemics models. We explore mostly the susceptible-infectious-susceptible (SIS) model, which can be readily treated with the CME as a two-state. We show that this approach is more accurate than individual based and pair based mean field methods, and a previously published dynamic message passing scheme. We explore average case predictions and extend the cavity master equation to SIR and SIRS models.

We perform a large scale analysis of a list of fintech terms in (i) news and blogs in English language and (ii) professional descriptions of companies operating in many countries. The occurrence and co-occurrence of fintech terms and locutions shows a progressive evolution of the list of fintech terms in a compact and coherent set of terms used worldwide to describe fintech business activities. By using methods of complex networks that are specifically designed to deal with heterogeneous systems, our analysis of a large set of professional descriptions of companies shows that companies having fintech terms in their description present over-expressions of specific attributes of country, municipality, and economic sector. By using the approach of statistically validated networks, we detect geographical and economic over-expressions of a set of companies related to the multi-industry, geographically and economically distributed fintech movement.

Situations involving cooperative behaviour are widespread among animals and humans alike. Game theory and evolutionary dynamics have provided the theoretical and computational grounds to understand what are the mechanisms that allow for such cooperation. Studies in this area usually take into consideration different behavioural strategies and investigate how they can be fixed in the population under evolving rules. However, how those strategies emerged from basic evolutionary mechanisms continues to be not fully understood. To address this issue, here we study the emergence of cooperative strategies through a model of heuristics selection based on evolutionary algorithms. In the proposed model, agents interact with other players according to a heuristic specified by their genetic code and reproduce -- at a longer time scale -- proportionally to their fitness. We show that the system can evolve to cooperative regimes for low mutation rates through heuristics selection while increasing the mutation decreases the level of cooperation. Our analysis of possible strategies shows that reciprocity and punishment are the main ingredients for cooperation to emerge, being conditional cooperation the more frequent strategy. Additionally, we show that if in addition to behavioural rules, genetic relatedness is included, then kinship plays a relevant role. Our results illustrate that our evolutionary heuristics model is a generic and powerful tool to study the evolution of cooperative behaviour.

The spread of pandemics such as COVID-19 is strongly linked to human activities. The objective of this paper is to specify and examine early indicators of disease spread risk in cities during the initial stages of outbreak based on patterns of human activities obtained from digital trace data. In this study, the Venables distance (D_v), and the activity density (D_a) are used to quantify and evaluate human activities for 193 US counties, whose cumulative number of confirmed cases was greater than 100 as of March 31, 2020. Venables distance provides a measure of the agglomeration of the level of human activities based on the average distance of human activities across a city or a county (less distance could lead to a greater contact risk). Activity density provides a measure of level of overall activity level in a county or a city (more activity could lead to a greater risk). Accordingly, Pearson correlation analysis is used to examine the relationship between the two human activity indicators and the basic reproduction number in the following weeks. The results show statistically significant correlations between the indicators of human activities and the basic reproduction number in all counties, as well as a significant leader-follower relationship (time lag) between them. The results also show one to two weeks' lag between the change in activity indicators and the decrease in the basic reproduction number. This result implies that the human activity indicators provide effective early indicators for the spread risk of the pandemic during the early stages of the outbreak. Hence, the results could be used by the authorities to proactively assess the risk of disease spread by monitoring the daily Venables distance and activity density in a proactive manner.