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In this work we analyze traces of mobility and co-location among a group of nearly 1000 closely interacting individuals. We attempt to reconstruct the Facebook friendship graph, Facebook interaction network, as well as call and SMS networks…
Generalization is a central aspect of learning theory. Here, we propose a framework that explores an auxiliary task-dependent notion of generalization, and attempts to quantitatively answer the following question: given two sets of patterns…
Recently, we introduced in arXiv:1105.2434 a model for product adoption in social networks with multiple products, where the agents, influenced by their neighbours, can adopt one out of several alternatives. We identify and analyze here…
The modeling of probability distributions, specifically generative modeling and density estimation, has become an immensely popular subject in recent years by virtue of its outstanding performance on sophisticated data such as images and…
Social networks have been of much interest in recent years. We here focus on a network structure derived from co-occurrences of people in traditional newspaper media. We find three clear deviations from what can be expected in a random…
Large-scale social networks constructed using contact metadata have been invaluable tools for understanding and testing social theories of society-wide social structures. However, multiplex relationships explaining different social contexts…
Assortative mixing in networks is the tendency for nodes with the same attributes, or metadata, to link to each other. It is a property often found in social networks manifesting as a higher tendency of links occurring between people with…
This paper is devoted to the mathematical study of some divergences based on the mutual information well-suited to categorical random vectors. These divergences are generalizations of the "entropy distance" and "information distance". Their…
Different network models have been suggested for the topology underlying complex interactions in natural systems. These models are aimed at replicating specific statistical features encountered in real-world networks. However, it is rarely…
Understanding how cooperation evolves in structured populations remains a fundamental question across diverse disciplines. The problem of cooperation typically involves pairwise or group interactions among individuals. While prior studies…
The analysis of social networks, in particular those describing face-to-face interactions between individuals, is complex due to the intertwining of the topological and temporal aspects. We revisit them both, using public data recorded by…
Citation and coauthor networks offer an insight into the dynamics of scientific progress. We can also view them as representations of a causal structure, a logical process captured in a graph. From a causal perspective, we can ask questions…
The popularity of federated learning comes from the possibility of better scalability and the ability for participants to keep control of their data, improving data security and sovereignty. Unfortunately, sharing model updates also creates…
Centrality describes the importance of nodes in a graph and is modeled by various measures. Its global analogue, called centralization, is a general formula for calculating a graph-level centrality score based on the node-level centrality…
We describe a complete theory for walk-based centrality indices in complex networks defined in terms of Mittag-Leffler functions. This overarching theory includes as special cases well-known centrality measures like subgraph centrality and…
Social media allow for an unprecedented amount of interaction between people online. A fundamental aspect of human social behavior, however, is the tendency of people to associate themselves with like-minded individuals, forming homogeneous…
It is known that up to certain pathologies, a compact metric graph with standard vertex conditions has a Baire-generic set of choices of edge lengths such that all Laplacian eigenvalues are simple and have eigenfunctions that do not vanish…
Thanks to widely available, cheap Internet access and the ubiquity of smartphones, millions of people around the world now use online location-based social networking services. Understanding the structural properties of these systems and…
Deep neural networks are often seen as different from other model classes by defying conventional notions of generalization. Popular examples of anomalous generalization behaviour include benign overfitting, double descent, and the success…
Detecting and exploiting similarities between seemingly distant objects is without doubt an important human ability. This paper develops \textit{from the ground up} an abstract algebraic and qualitative notion of similarity based on the…