Recently, hyperbolic deep neural networks (HDNNs) have been gaining momentum as the
deep representations in the hyperbolic space provide high fidelity embeddings with few …

Networks are finite metric spaces, with distances defined by the shortest paths between
nodes. However, this is not the only form of network geometry: two others are the geometry …

We introduce Mercator, a reliable embedding method to map real complex networks into
their hyperbolic latent geometry. The method assumes that the structure of networks is well …

Symmetries in physical theories denote invariance under some transformation, such as self-
similarity under a change of scale. The renormalization group provides a powerful …

Reducing dimension redundancy to find simplifying patterns in high-dimensional datasets
and complex networks has become a major endeavor in many scientific fields. However …

Protected areas underpin global biodiversity conservation and sustainability agendas.
Biological invasions increasingly threaten the ecological functioning and long-term …

Delamination or crack are standard failure patterns of composite T-joints. Most existing
studies focus on pull-off loaded composite T-joint cracking but little focus on adverse …

The evolution processes of complex systems carry key information in the systems' functional
properties. Applying machine learning algorithms, we demonstrate that the historical …

One of the pillars of the geometric approach to networks has been the development of model-
based mapping tools that embed real networks in its latent geometry. In particular, the tool …

Turing patterns, arising from the interplay between competing species of diffusive particles,
have long been an important concept for describing nonequilibrium self-organization in …