Modelling brain connectomes networks: Solv is a worthy competitor to hyperbolic geometry!
This work addresses the challenge of accurately modeling neural connections for researchers in neuroscience and network science, though it is incremental as it extends existing geometric approaches.
The paper tackled the problem of embedding brain connectome networks by comparing various geometries, including Solv, and found that while 3D hyperbolic embeddings often perform best, Solv embeddings are a competitive alternative.
Finding suitable embeddings for connectomes (spatially embedded complex networks that map neural connections in the brain) is crucial for analyzing and understanding cognitive processes. Recent studies have found two-dimensional hyperbolic embeddings superior to Euclidean embeddings in modeling connectomes across species, especially human connectomes. However, those studies had limitations: geometries other than Euclidean, hyperbolic, or spherical were not considered. Following William Thurston's suggestion that the networks of neurons in the brain could be successfully represented in Solv geometry, we study the goodness-of-fit of the embeddings for 21 connectome networks (8 species). To this end, we suggest an embedding algorithm based on Simulating Annealing that allows us to embed connectomes to Euclidean, Spherical, Hyperbolic, Solv, Nil, and product geometries. Our algorithm tends to find better embeddings than the state-of-the-art, even in the hyperbolic case. Our findings suggest that while three-dimensional hyperbolic embeddings yield the best results in many cases, Solv embeddings perform reasonably well.