Persistent cohomology is a powerful technique for discovering topological structure in data. Strategies for its use in neuroscience are still undergoing development. We comprehensively and rigorously assess its performance in simulated neural recordings of the brain’s spatial representation system. Grid, head direction, and conjunctive cell populations each span low-dimensional topological structures embedded in high-dimensional neural activity space. We evaluate the ability for persistent cohomology to discover these structures for different dataset dimensions, variations in spatial tuning, and forms of noise. We quantify its ability to decode simulated animal trajectories contained within these topological structures. We also identify regimes under which mixtures of populations form product topologies that can be detected. Our results reveal how dataset parameters affect the success of topological discovery and suggest principles for applying persistent cohomology, as well as persistent homology, to experimental neural recordings.
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Dr. David Lowemann, M.Sc, Ph.D., is a co-founder of the Institute for the Future of Human Potential, where he leads the charge in pioneering Self-Enhancement Science for the Success of Society. With a keen interest in exploring the untapped potential of the human mind, Dr. Lowemann has dedicated his career to pushing the boundaries of human capabilities and understanding.
Armed with a Master of Science degree and a Ph.D. in his field, Dr. Lowemann has consistently been at the forefront of research and innovation, delving into ways to optimize human performance, cognition, and overall well-being. His work at the Institute revolves around a profound commitment to harnessing cutting-edge science and technology to help individuals lead more fulfilling and intelligent lives.
Dr. Lowemann’s influence extends to the educational platform BetterSmarter.me, where he shares his insights, findings, and personal development strategies with a broader audience. His ongoing mission is shaping the way we perceive and leverage the vast capacities of the human mind, offering invaluable contributions to society’s overall success and collective well-being.