In this study, we investigated cancer cellular networks in the context of gene interactions and their associated patterns in order to recognize the structural features underlying this disease. We aim to propose that the quest of understanding cancer takes us beyond pairwise interactions between genes to a higher-order construction. We characterize the most prominent network deviations in the gene interaction patterns between cancer and normal samples that contribute to the complexity of this disease. What we hope is that through understanding these interaction patterns we will notice a deeper structure in the cancer network. This study uncovers the significant deviations that topological features in cancerous cells show from the healthy one, where the last stage of filtration confirms the importance of one-dimensional holes (topological loops) in cancerous cells and two-dimensional holes (topological voids) in healthy cells. In the small threshold region, the drop in the number of connected components of the cancer network, along with the rise in the number of loops and voids, all occurring at some smaller weight values compared to the normal case, reveals the cancerous network tendency to certain pathways.

Genes communicate with each other through different regulatory effects, which lead to the emergence of complex network structures in cells, and such structures are expected to be different for normal and cancerous cells. To study these differences, we have investigated the Gene Regulatory Network (GRN) of cells as inferred from RNA-sequencing data. The GRN is a signed weighted network corresponding to the inductive or inhibitory interactions. Here we focus on a particular of motifs in the GRN, the triangles, which are imbalanced if the number of negative interactions is odd. By studying the stability of imbalanced triangles in the GRN, we show that the network of cancerous cells has fewer imbalanced triangles compared to normal cells. Moreover, in the normal cells, imbalanced triangles are isolated from the main part of the network, while such motifs are part of the network's giant component in cancerous cells. Our result demonstrates that due to genes' collective behavior the structure of the complex networks is different in cancerous cells from those in normal ones.

We study how the herd immunity threshold and the expected epidemic size depend on homophily with respect to vaccine adoption. We find that the presence of homophily considerably increases the critical vaccine coverage needed for herd immunity and that strong homophily can push the threshold entirely out of reach. The epidemic size monotonically increases as a function of homophily strength for a perfect vaccine, while it is maximized at a nontrivial level of homophily when the vaccine efficacy is limited. Our results highlight the importance of vaccination homophily in epidemic modeling.

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Fully decentralised federated learning enables collaborative training of individual machine learning models on distributed devices on a network while keeping the training data localised. This approach enhances data privacy and eliminates both the single point of failure and the necessity for central coordination. Our research highlights that the effectiveness of decentralised federated learning is significantly influenced by the network topology of connected devices. A simplified numerical model for studying the early behaviour of these systems leads us to an improved artificial neural network initialisation strategy, which leverages the distribution of eigenvector centralities of the nodes of the underlying network, leading to a radically improved training efficiency. Additionally, our study explores the scaling behaviour and choice of environmental parameters under our proposed initialisation strategy. This work paves the way for more efficient and scalable artificial neural network training in a distributed and uncoordinated environment, offering a deeper understanding of the intertwining roles of network structure and learning dynamics.