Modelling brain connectomes networks: Solv is a worthy competitor to hyperbolic geometry!

Dorota Celińska-Kopczyńska, Eryk Kopczyński

Primary Area: applications to neuroscience & cognitive science

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Keywords: Solv geometry, hyperbolic embeddings, connectomes

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TL;DR: analysis of the embeddings of brain networks into Thurston geometries obtained using simulated annealing

Abstract:

Finding suitable embeddings for connectomes (spatially embedded complex networks that map neural conections in the brain) is crucial for analyzing and understanding cognitive processes. Recent studies has found two-dimensional hyperbolic embeddings superior to Euclidean embeddings in modelling connectomes across species, especially human connectomes. However, those studies had some limitations: geometries other than Euclidean, hyperbolic or spherical were not taken into account. Following the suggestion of William Thurston that the
networks of neurons in the brain could be sucessfully represented in Solv geometry, we study 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 embed connectomes to Euclidean, Spherical, Hyperbolic, Solv, Nil, and also 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 in many cases, three-dimensional hyperbolic embeddings yield the best results, Solv embeddings perform reasonably well.

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Submission Number: 57