Simplex polynomial in complex networks and its applications to compute the Euler characteristic

In algebraic topology, a k-dimensional simplex is defined as a convex polytope consisting of k + 1 vertices. If spatial dimensionality is not considered, it corresponds to the complete graph with k + 1 vertices in graph theory. The alternating sum of the number of simplices across dimensions yields a topological invariant known as the Euler characteristic, which has gained significant attention due to its widespread application in fields such as topology, homology theory, complex systems, and...
Read more...

A neural network model combining the successor representation and actor-critic methods reveals effective biological use of the representation

In learning goal-directed behavior, state representation is important for adapting to the environment and achieving goals. A predictive state representation called successive representation (SR) has recently attracted attention as a candidate for state representation in animal brains, especially in the hippocampus. The relationship between the SR and the animal brain has been studied, and several neural network models for computing the SR have been proposed based on the findings. However,...
Read more...