Reducing redundant information to find simplifying patterns in data sets and complex networks is a scientific challenge in many knowledge fields. Moreover, detecting the dimensionality of the data is ...

Mathematicians often comment on the beauty of their chosen discipline. For the non-mathematicians among us, that can be hard to visualise. But in Prof Caroline Series’s field of hyperbolic geometry, ...

Complex networks, ranging from biological systems to technological and social infrastructures, have long intrigued researchers with their intricate connectivity and emergent behaviours. Recent ...

Complex hyperbolic geometry investigates spaces that combine the subtleties of complex structures with non‐Euclidean, negatively curved metrics, offering rich terrain for both theoretical exploration ...

Dependencies are identified in two recently proposed first-order axiom systems for plane hyperbolic geometry. Since the dependencies do not specifically concern hyperbolic geometry, our results yield ...

This is a preview. Log in through your library . Abstract In this paper we investigate angle geometry in the universal Teichmüller space. We construct three examples of triangles bounded by geodesic ...

Hyperbolic space is a Pringle-like alternative to flat, Euclidean geometry where the normal rules don’t apply: angles of a triangle add up to less than 180 degrees and Euclid’s parallel postulate, ...