🍩 Database of Original & Non-Theoretical Uses of Topology

(found 2 matches in 0.001232s)

  1. What Can Topology Tell Us About the Neural Code? (2017)

    Carina Curto
    Abstract Neuroscience is undergoing a period of rapid experimental progress and expansion. New mathematical tools, previously unknown in the neuroscience community, are now being used to tackle fundamental questions and analyze emerging data sets. Consistent with this trend, the last decade has seen an uptick in the use of topological ideas and methods in neuroscience. In this paper I will survey recent applications of topology in neuroscience, and explain why topology is an especially natural tool for understanding neural codes.

  2. Clique Topology Reveals Intrinsic Geometric Structure in Neural Correlations (2015)

    Chad Giusti, Eva Pastalkova, Carina Curto, Vladimir Itskov
    Abstract Detecting structure in neural activity is critical for understanding the function of neural circuits. The coding properties of neurons are typically investigated by correlating their responses to external stimuli. It is not clear, however, if the structure of neural activity can be inferred intrinsically, without a priori knowledge of the relevant stimuli. We introduce a novel method, called clique topology, that detects intrinsic structure in neural activity that is invariant under nonlinear monotone transformations. Using pairwise correlations of neurons in the hippocampus, we demonstrate that our method is capable of detecting geometric structure from neural activity alone, without appealing to external stimuli or receptive fields.Detecting meaningful structure in neural activity and connectivity data is challenging in the presence of hidden nonlinearities, where traditional eigenvalue-based methods may be misleading. We introduce a novel approach to matrix analysis, called clique topology, that extracts features of the data invariant under nonlinear monotone transformations. These features can be used to detect both random and geometric structure, and depend only on the relative ordering of matrix entries. We then analyzed the activity of pyramidal neurons in rat hippocampus, recorded while the animal was exploring a 2D environment, and confirmed that our method is able to detect geometric organization using only the intrinsic pattern of neural correlations. Remarkably, we found similar results during nonspatial behaviors such as wheel running and rapid eye movement (REM) sleep. This suggests that the geometric structure of correlations is shaped by the underlying hippocampal circuits and is not merely a consequence of position coding. We propose that clique topology is a powerful new tool for matrix analysis in biological settings, where the relationship of observed quantities to more meaningful variables is often nonlinear and unknown.