Year: 2018
Type: article
Abstract: Data analysis techniques from network science have fundamentally improved our understanding of neural systems and the complex behaviors that they support. Yet the restriction of network techniques to the study of pairwise interactions prevents us from taking into account intrinsic topological features such as cavities that may be crucial for system function. To detect and quantify these topological features, we must turn to algebro-topological methods that encode data as a simplicial complex built from sets of interacting nodes called simplices. We then use the relations between simplices to expose cavities within the complex, thereby summarizing its topological features. Here we provide an introduction to persistent homology, a fundamental method from applied topology that builds a global descriptor of system structure by chronicling the evolution of cavities as we move through a combinatorial object such as a weighted network. We detail the mathematics and perform demonstrative calculations on the mouse structural connectome, synapses in C. elegans, and genomic interaction data. Finally, we suggest avenues for future work and highlight new advances in mathematics ready for use in neural systems.
Source: Network Neuroscience
DOI: 10.1162/netn_a_00073
Institution: University of Pennsylvania
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,750
Funders: National Science Foundation, John D. and Catherine T. MacArthur Foundation, Alfred P. Sloan Foundation, Paul G. Allen Family Foundation, Institute for Scientific Interchange, National Institutes of Health, Office of Naval Research, National Institute of Mental Health, National Institute on Deafness and Other Communication Disorders, National Institute of General Medical Sciences, National Institute of Neurological Disorders and Stroke, National Institute of Child Health and Human Development, Eunice Kennedy Shriver National Institute of Child Health and Human Development, Army Research Office, Army Research Laboratory
Awards: G1001159199, G1024130705, G1028610982, G1041393086, Multimodal brain maturation indices modulating psychopathology and neurocognition, G1099660080, G1177916794, G1184818683, G129050353, G129985460, G1350070852, G1483473580, G155546341, G157307749, G1630141903, G1778482337, G1929728195, G1993459732, G2066955304, G2130352337, G2236980202, Virtual Resection to Treat Epilepsy, G2244810882, G2247336289, G2252567680, G235261508, G2425642435, G2481140831, G2519463293, G2668337057, G2792366995, G2864901048, G2887601406, G2901702611, G2942273589, G3137615481, G3141641755, G3330175468, G334592757, G3424441068, G3437992771, G3564833335, G3574985532, G3611952402, G3690479056, G3755125221, G3824545241, G4069802742, Statistical Methods for High-Resolution Multiscale Analysis in DNA Interactions, G4473135385, G4652607670, G4823423002, G5036215508, G5172716836, G5253651465, G5259331294, G5389825636, G5419322094, G5469137442, G5496178531, G5721726644, G572628577, G5760707814, NCS-FO: Collaborative Research: A Mechanistic Model of Cognitive Control, G5884259427, CAREER: Linking Graph Topology of Learned Information to Behavioral Variability via Dynamics of Functional Brain Networks, G6446615898, G6467593695, G656215873, G657448715, CRCNS: Collaborative Research: Mapping and Control of Large-Scale Neural Dynamics, G6689184838, G6752185412, Linguistic and Nonlinguistic Functions of Frontal Cortex, G6981911394, G701307588, G709716657, Evolution of the Linked Architecture of Network Control and Executive Function in Adolescence, G7159985717, G7236036932, G7452299184, WORKSHOP: Quantitative Theories of Learning, Memory, and Prediction, G7530591242, G7538535954, G7594130654, G7747382488, G7838535007, G7881329, G793584043, G7989609580, G8164210364, G8454816522, CRCNS: US-France Modeling & Predicting BCI Learning from Dynamic Networks, G8554419822, G8796586358, G8876996369, G8895310522, Inter-modal Coupling Image Analytics, G90128336, G912920117, G91481811, G916315028, G91658921
OpenAlex ID: W2807785447