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Topology of cognitive maps
In present paper we discuss several approaches to reconstructing the topology of the physical space from neural activity data of CA1 fields in mice hippocampus, in particular, having Cognitome theory of brain function in mind.
Topology and geometry of data manifold in deep learning
Despite significant advances in the field of deep learning in applications to various fields, explaining the inner processes of deep learning models remains an important and open question.
Dimensions of multi-fan algebras
Given an arbitrary non-zero simplicial cycle and a generic vector coloring of its vertices, there is a way to produce a graded Poincare duality algebra associated with these data.
Combinatorics Commutative Algebra Algebraic Topology Geometric Topology Primary 05E40, 05E45, 28A75, 57M27, Secondary 13H10, 13P20, 13D40, 52C35, 52B70, 57N65, 13A02, 57M25, 05C15
