Cooperative behaviour in complex systems

In my PhD thesis I studied cooperative phenomena arise in complex systems using the methods of statistical and computational physics. The aim of my work was also to study the critical behaviour of interacting many-body systems during their phase transitions and describe their universal features analytically and by means of numerical calculations. In order to do so I completed studies in four different subjects. My first investigated subject was a study of non-equilibrium phase transitions in weighted scale-free networks. The second problem I examined was the ferromagnetic random bond Potts model with large values of q on evolving scale-free networks which problem is equivalent to an optimal cooperation problem. The third examined problem was related to the large-q sate random bond Potts model also and I examined the critical density of clusters which touched a certain border of a perpendicular strip like geometry and expected to hold analytical forms deduced from conformal invariance. The last investigated problem was a study of the non-equilibrium dynamical behaviour of the antiferromagnetic Ising model on two-dimensional triangular lattice at zero temperature in the absence of external field and at the Kosterlitz-Thouless phase transition point.Comment: PhD thesis, 155 pages, 42 figure

From calls to communities: a model for time varying social networks

Social interactions vary in time and appear to be driven by intrinsic mechanisms, which in turn shape the emerging structure of the social network. Large-scale empirical observations of social interaction structure have become possible only recently, and modelling their dynamics is an actual challenge. Here we propose a temporal network model which builds on the framework of activity-driven time-varying networks with memory. The model also integrates key mechanisms that drive the formation of social ties - social reinforcement, focal closure and cyclic closure, which have been shown to give rise to community structure and the global connectedness of the network. We compare the proposed model with a real-world time-varying network of mobile phone communication and show that they share several characteristics from heterogeneous degrees and weights to rich community structure. Further, the strong and weak ties that emerge from the model follow similar weight-topology correlations as real-world social networks, including the role of weak ties.Comment: 10 pages, 5 figure

The Scaling of Human Contacts in Reaction-Diffusion Processes on Heterogeneous Metapopulation Networks

We present new empirical evidence, based on millions of interactions on Twitter, confirming that human contacts scale with population sizes. We integrate such observations into a reaction-diffusion metapopulation framework providing an analytical expression for the global invasion threshold of a contagion process. Remarkably, the scaling of human contacts is found to facilitate the spreading dynamics. Our results show that the scaling properties of human interactions can significantly affect dynamical processes mediated by human contacts such as the spread of diseases, and ideas

Social inequalities that matter for contact patterns, vaccination, and the spread of epidemics

Individuals socio-demographic and economic characteristics crucially shape the spread of an epidemic by largely determining the exposure level to the virus and the severity of the disease for those who got infected. While the complex interplay between individual characteristics and epidemic dynamics is widely recognized, traditional mathematical models often overlook these factors. In this study, we examine two important aspects of human behavior relevant to epidemics: contact patterns and vaccination uptake. Using data collected during the Covid-19 pandemic in Hungary, we first identify the dimensions along which individuals exhibit the greatest variation in their contact patterns and vaccination attitudes. We find that generally privileged groups of the population have higher number of contact and a higher vaccination uptake with respect to disadvantaged groups. Subsequently, we propose a data-driven epidemiological model that incorporates these behavioral differences. Finally, we apply our model to analyze the fourth wave of Covid-19 in Hungary, providing valuable insights into real-world scenarios. By bridging the gap between individual characteristics and epidemic spread, our research contributes to a more comprehensive understanding of disease dynamics and informs effective public health strategies.Comment: 33 pages, 22 figure

Detecting periodic time scales in temporal networks

Temporal networks are commonly used to represent dynamical complex systems like social networks, simultaneous firing of neurons, human mobility or public transportation. Their dynamics may evolve on multiple time scales characterising for instance periodic activity patterns or structural changes. The detection of these time scales can be challenging from the direct observation of simple dynamical network properties like the activity of nodes or the density of links. Here we propose two new methods, which rely on already established static representations of temporal networks, namely supra-adjacency matrices and temporal event graphs. We define dissimilarity metrics extracted from these representations and compute their Fourier Transform to effectively identify dominant periodic time scales characterising the original temporal network. We demonstrate our methods using synthetic and real-world data sets describing various kinds of temporal networks. We find that while in all cases the two methods outperform the reference measures, the supra-adjacency based method identifies more easily periodic changes in network density, while the temporal event graph based method is better suited to detect periodic changes in the group structure of the network. Our methodology may provide insights into different phenomena occurring at multiple time-scales in systems represented by temporal networks.Comment: 19 pages, 11 figure

Interpreting wealth distribution via poverty map inference using multimodal data

Poverty maps are essential tools for governments and NGOs to track socioeconomic changes and adequately allocate infrastructure and services in places in need. Sensor and online crowd-sourced data combined with machine learning methods have provided a recent breakthrough in poverty map inference. However, these methods do not capture local wealth fluctuations, and are not optimized to produce accountable results that guarantee accurate predictions to all sub-populations. Here, we propose a pipeline of machine learning models to infer the mean and standard deviation of wealth across multiple geographically clustered populated places, and illustrate their performance in Sierra Leone and Uganda. These models leverage seven independent and freely available feature sources based on satellite images, and metadata collected via online crowd-sourcing and social media. Our models show that combined metadata features are the best predictors of wealth in rural areas, outperforming image-based models, which are the best for predicting the highest wealth quintiles. Our results recover the local mean and variation of wealth, and correctly capture the positive yet non-monotonous correlation between them. We further demonstrate the capabilities and limitations of model transfer across countries and the effects of data recency and other biases. Our methodology provides open tools to build towards more transparent and interpretable models to help governments and NGOs to make informed decisions based on data availability, urbanization level, and poverty thresholds.Comment: 12 pages. In Proceedings of the ACM Web Conference 2023 (WWW'23