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Small-world architectures may be implicated in a range of phenomena from disease propagation to networks of neurons in the cerebral cortex. While most of the recent attention on small-world networks has focussed on the effect of introducing…
We address the problem of diversification in religions by studying selection on cultural memes that colonize humans hosts. In analogy to studying the evolution of pathogens or symbionts colonizing animal hosts, we use models for…
Community structures have been identified in various complex real-world networks, for example, communication, information, internet and shareholder networks. The scaling of community size distribution indicates the heterogeneity in the…
Phylogenetic trees in genetics and biology in general are all binary. We make an attempt to answer one fundamental question: Is such binary branching from the coarsest to the finest scales sustained by data? We convert this question into an…
Different people and cultures associate different emotional states to different parts and spaces of cities. These vary according to individuals, their cultures and also to the time of day, day of week, season, special occasions and more.…
Clusters or communities can provide a coarse-grained description of complex systems at multiple scales, but their detection remains challenging in practice. Community detection methods often define communities as dense subgraphs, or…
In a complex system, the individual components are neither so tightly coupled or correlated that they can all be treated as a single unit, nor so uncorrelated that they can be approximated as independent entities. Instead, patterns of…
An outstanding open problem is whether collective social phenomena occurring over short timescales can systematically reduce cultural heterogeneity in the long run, and whether offline and online human interactions contribute differently to…
Strategic diagrams and co-word analysis are widely employed to examine the conceptual structure of scientific domains and their development over time. Yet a structural inconsistency characterises dominant longitudinal implementations:…
Interactions are ubiquitous across biological systems. These interactions can be abstracted as patterns of connections among distinct units such as genes, proteins, individual organisms, or species which form a hierarchy of biological…
Evolution has fascinated quantitative and physical scientists for decades: how can the random process of mutation, recombination, and duplication of genetic information generate the diversity of life? What determines the rate of evolution?…
The intriguing nature of classical Homeric narratives has always fascinated the occidental culture contributing to philosophy, history, mythology and straight forwardly to literature. However what would be so intriguing about Homer's…
The human niche represents the intersection of biological, ecological, cultural, and technological processes that have co-evolved to shape human adaptation and societal complexity. This paper explores the human niche through the lens of…
Successful innovations achieve large geographical coverage by spreading across settlements and distances. For decades, spatial diffusion has been argued to take place along the urban hierarchy such that the innovation first spreads from…
Emergence of self-similarity in hierarchical community structures is ubiquitous in complex systems. Yet, there is a dearth of universal quantification and general principles describing the formation of such structures. Here, we discover…
Multiple scales coexist in complex networks. However, the small world property makes them strongly entangled. This turns the elucidation of length scales and symmetries a defiant challenge. Here, we define a geometric renormalization group…
Heterogeneous and complex networks represent intertwined interactions between real-world elements or agents. Determining the multi-scale mesoscopic organization of clusters and intertwined structures is still a fundamental and open problem…
We study hierarchical clusterings of metric spaces that change over time. This is a natural geometric primitive for the analysis of dynamic data sets. Specifically, we introduce and study the problem of finding a temporally coherent…
The topology of any complex system is key to understanding its structure and function. Fundamentally, algebraic topology guarantees that any system represented by a network can be understood through its closed paths. The length of each path…
Systems as diverse as genetic networks or the world wide web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This…