Spaces and sequences in the hippocampus: a homological perspective

Area of Science:

• Neuroscience
• Computational Neuroscience
• Cognitive Science

Background:

• Topological techniques, like simplicial homology, are used to study neural information flow and cognitive map formation.
• Cognitive functions are increasingly understood to be supported by serial patterns of neural activity.
• Existing methods often require prior assumptions about the nature or function of these activity sequences.

Purpose of the Study:

• To investigate serial patterns of neuronal activity in the hippocampus using path homology theory.
• To provide a universal, assumption-free approach for analyzing the ordinal arrangement of neural activity sequences.
• To compare sequential activity patterns with topological structures in the hippocampus during spatial learning.

Main Methods:

• Application of path homology theory to quantify the ordinal arrangement of neuronal activity sequences in the hippocampus.
• Analysis of sequence consolidation and stability over timescales relevant to spatial learning.
• Comparison of ordinal maps with topological maps derived from simplicial homologies.

Main Results:

• The vast majority of spatial navigation sequences in the hippocampus are structurally equivalent.
• A few distinct classes of sequences, built from short activity motifs, form a stable ordinal schema.
• This ordinal organization emerges and stabilizes on timescales characteristic of spatial learning.

Conclusions:

• Path homology theory offers a powerful framework for analyzing sequential neural activity without a priori assumptions.
• Hippocampal spatial navigation relies on a limited set of stable, short-motif-based sequential patterns.
• Ordinal and topological analyses capture distinct, complementary aspects of neural information processing.