The complexity of many biological, social and technological systems stems from the richness
of the interactions among their units. Over the past decades, a variety of complex systems …

Advances in experimental neuroscience have transformed our ability to explore the structure
and function of neural circuits. At the same time, advances in machine learning have …

Humans and animals use mental representations of the spatial structure of the world to
navigate. The classical view is that these representations take the form of Euclidean …

BACKGROUND Ever since Edward Tolman's proposal that comprehensive cognitive maps
underlie spatial navigation and, more generally, psychological functions, the question of …

The'cognitive map'hypothesis proposes that brain builds a unified representation of the
spatial environment to support memory and guide future action. Forty years of …

The last decade has produced exciting new ideas about retrosplenial cortex (RSC) and its
role in integrating diverse inputs. Here, we review the diversity in forms of spatial and …

Topological data analysis (TDA) can broadly be described as a collection of data analysis
methods that find structure in data. These methods include clustering, manifold estimation …

Persistent homology (PH) is a method used in topological data analysis (TDA) to study
qualitative features of data that persist across multiple scales. It is robust to perturbations of …

The language of graph theory, or network science, has proven to be an exceptional tool for
addressing myriad problems in neuroscience. Yet, the use of networks is predicated on a …

Topological networks lie at the heart of our cities and social milieu. However, it remains
unclear how and when the brain processes topological structures to guide future behaviour …