A study published in Nature Communications and directed by Professor Carlo Vittorio Cannistraci, director of the Center for Complex Network Intelligence (CCNI) at the Tsinghua Laboratory of Brain and Intelligence, proposes a fast algorithm to measure the relation between the variables space of an interconnected complex system, its geometry and its navigability, revealing why this can enhance our understanding of the brain differences across age and sex.
Many variables shape the connectivity of networks associated with complex systems such as human society.
Some of these variables are commonly known, for instance, the greater the popularity of a person the larger the number of connections he or she can have on social media networks.
Another example is given by variables such as semantic or spatial proximity. The more people share common interests or live in areas geographically close together, the higher the probability that they link and cluster together forming small and medium communities in a network.
If variables such as popularity and proximity are known, many other variables that shape the connectivity of the network in a complex system are unknown, but the geometrical relation of these variables in a multidimensional space remains imprinted as a ‘trace’ in the network structure.
“If physics studies the principles and mechanisms of the outside universe, brain science studies the principles and mechanisms of the inside universe,” said Cannistraci who is the first author of the study. “My research is at the interface between these two disciplines. I deal with Physics and Engineering of Complexity and Intelligence: studying principles of natural and artificial intelligence.”
In the study, which has now been published in the scientific journal Nature Communications, Cannistraci envisioned and realized with the assistance of co-author Alessandro Muscoloni, how to build an optimized algorithm that reduces 26 years worst scenario of computation to 1 week, being able to measure the extent to which a network topology is congruent with an associated manifold geometry.
The manifold represents the rule of geometrical associations between all the variables that contribute to forming the network’s shape in a complex system, and the network is a sort of discretization of this manifold.
The hidden geometry of the manifold behind the structure of brain networks is unknown.
“Although we visualize brain networks in a three-dimensional space, the number of variables that shape their architecture is higher,” said Cannistraci.
“Some of these variables such as age and sex are known, but many others are unknown, nevertheless, we can still find their trace in the shape of the brain network, therefore we can try to measure how congruent is the shape of a network with its hidden geometry,” said Cannistraci. “This measure can be used as a marker that can differentiate different states or conditions of brain networks, and therefore can help to envision new theories and measures to design markers for brain diseases.: