The ability to store and manipulate information is a hallmark of computational systems.
Whereas computers are carefully engineered to represent and perform mathematical …

Hopfield networks are artificial neural networks which store memory patterns on the states of
their neurons by choosing recurrent connection weights and update rules such that the …

We present a viable geometric solution for the detection of dynamic effects in complex
networks. Building on Forman's discretization of the classical notion of Ricci curvature, we …

Hypergraphs serve as models of complex networks that capture more general structures
than binary relations. For graphs, a wide array of statistics has been devised to gauge …

We describe an approach to the analysis of chemical (and other) networks that, in contrast to
other schemes, is based on edges rather than vertices, naturally works with directed and …

The human brain forms functional networks on all spatial scales. Modern fMRI scanners
allow to resolve functional brain data in high resolutions, allowing to study large-scale …

Memory is a complex process that spans multiple time-scales and stages, and, as expected,
involves multiple brain regions. Traditionally, computational models of memory are either too …

Computational modeling of the neural activity in the human spinal cord may help elucidate
the underlying mechanisms involved in the complex processing of painful stimuli. In this …

We employ the Hopfield model as a simplified framework to explore both the memory deficits
and the biochemical processes characteristic of Alzheimer's disease. By simulating neuronal …

Consider a sample of n points taken iid from a submanifold Σ of Euclidean space. We show
that there is a way to estimate the Ricci curvature of Σ with respect to the induced metric from …