Modelling brain connectomes networks: Solv is a worthy competitor to hyperbolic geometry! Dorota Celi nska-Kopczy nska, Eryk Kopczy nski Institute of Informatics, University of Warsaw, Warsaw, Poland July 24, 2024 Abstract 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 con-nectome networks (8 species). To this end, we suggest an embedding algorithm based on Simulating Annealing that allows us to embed con-nectomes 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. 1 Introduction Connectomes are comprehensive maps of the neural connections in the brain. Understanding the interactions they shape is a key to understanding cognitive processes. Given their spatially embedded complexity, shaped by physical 1 arXiv:2407.16077v1 Therefore, a vast amount of recent research has been devoted to finding the appropriate embeddings for con-nectome networks. Recent studies (e.g., [WHKL22, AS20]) have advocated for the superiority of two-dimensional hyperbolic embeddings over Euclidean embeddings in modeling connectomes across species, especially human con-nectomes. However, those studies had limitations: they restricted the focus to Euclidean, hyperbolic, or spherical geometries, neglecting to explore other potential embedding spaces.

Hyperbolic models can reproduce the heavy-tailed degree distribution, high clustering, and hierarchical structure of empirical networks. Current algorithms for finding the hyperbolic coordinates of networks, however, do not quantify uncertainty in the inferred coordinates. We present BIGUE, a Markov chain Monte Carlo (MCMC) algorithm that samples the posterior distribution of a Bayesian hyperbolic random graph model. We show that combining random walk and random cluster transformations significantly improves mixing compared to the commonly used and state-of-the-art dynamic Hamiltonian Monte Carlo algorithm. Using this algorithm, we also provide evidence that the posterior distribution cannot be approximated by a multivariate normal distribution, thereby justifying the use of MCMC to quantify the uncertainty of the inferred parameters.

Automatic off-line design is an attractive approach to implementing robot swarms. In this approach, a designer specifies a mission for the swarm, and an optimization process generates suitable control software for the individual robots through computer-based simulations. Most relevant literature has focused on effectively transferring control software from simulation to physical robots. For the first time, we investigate (i) whether control software generated via automatic design is transferable across robot platforms and (ii) whether the design methods that generate such control software are themselves transferable. We experiment with two ground mobile platforms with equivalent capabilities. Our measure of transferability is based on the performance drop observed when control software and/or design methods are ported from one platform to another. Results indicate that while the control software generated via automatic design is transferable in some cases, better performance can be achieved when a transferable method is directly applied to the new platform.

Petal has received a $13 million funding round from Valar Ventures, a New York-based venture capital fund that specializes in financial technology, to use artificial intelligence to fill holes in legacy risk vetting. "The problem is not that people have a history of bad credit, but have no history of credit at all," said Jason Gross, Petal's CEO. "They're young or have lacked access to financial services." Petal will use the funds to add scale for its formal launch. The company has been signing up prospective users since the fall and currently has about 40,000 consumers who preordered its alternative payment cards.