2016/01/07 by Chad Giusti, Robert Ghrist, Giusti, Chad +3 · 11 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · #57Q05 #92-02 #92B20 #Algebraic Topology (math.AT) #Cell Image Analysis Techniques #Data Visualization and Analytics #FOS: Biological sciences #FOS: Mathematics #Neurons and Cognition (q-bio.NC) #Quantitative Methods (q-bio.QM) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1601.01704
openalex publication_date 2016/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The language of graph theory, or network science, has proven to be an\nexceptional tool for addressing myriad problems in neuroscience. Yet, the use\nof networks is predicated on a critical simplifying assumption: that the\nquintessential unit of interest in a brain is a dyad -- two nodes (neurons or\nbrain regions) connected by an edge. While rarely mentioned, this fundamental\nassumption inherently limits the types of neural structure and function that\ngraphs can be used to model. Here, we describe a generalization of graphs that\novercomes these limitations, thereby offering a broad range of new\npossibilities in terms of modeling and measuring neural phenomena.\nSpecifically, we explore the use of \simplicial complexes, a theoretical\nnotion developed in the field of mathematics known as algebraic topology, which\nis now becoming applicable to real data due to a rapidly growing computational\ntoolset. We review the underlying mathematical formalism as well as the budding\nliterature applying simplicial complexes to neural data, from\nelectrophysiological recordings in animal models to hemodynamic fluctuations in\nhumans. Based on the exceptional flexibility of the tools and recent\nground-breaking insights into neural function, we posit that this framework has\nthe potential to eclipse graph theory in unraveling the fundamental mysteries\nof cognition.\n