🍩 Database of Original & Non-Theoretical Uses of Topology

(found 2 matches in 0.002205s)

  1. Topological Data Analysis of C. Elegans Locomotion and Behavior (2021)

    Ashleigh Thomas, Kathleen Bates, Alex Elchesen, Iryna Hartsock, Hang Lu, Peter Bubenik
    Abstract Video of nematodes/roundworms was analyzed using persistent homology to study locomotion and behavior. In each frame, an organism's body posture was represented by a high-dimensional vector. By concatenating points in fixed-duration segments of this time series, we created a sliding window embedding (sometimes called a time delay embedding) where each point corresponds to a sequence of postures of an organism. Persistent homology on the points in this time series detected behaviors and comparisons of these persistent homology computations detected variation in their corresponding behaviors. We used average persistence landscapes and machine learning techniques to study changes in locomotion and behavior in varying environments.

  2. Current Theoretical Models Fail to Predict the Topological Complexity of the Human Genome (2015)

    Javier Arsuaga, Reyka G. Jayasinghe, Robert G. Scharein, Mark R. Segal, Robert H. Stolz, Mariel Vazquez
    Abstract Understanding the folding of the human genome is a key challenge of modern structural biology. The emergence of chromatin conformation capture assays (e.g., Hi-C) has revolutionized chromosome biology and provided new insights into the three dimensional structure of the genome. The experimental data are highly complex and need to be analyzed with quantitative tools. It has been argued that the data obtained from Hi-C assays are consistent with a fractal organization of the genome. A key characteristic of the fractal globule is the lack of topological complexity (knotting or inter-linking). However, the absence of topological complexity contradicts results from polymer physics showing that the entanglement of long linear polymers in a confined volume increases rapidly with the length and with decreasing volume. In vivo and in vitro assays support this claim in some biological systems. We simulate knotted lattice polygons confined inside a sphere and demonstrate that their contact frequencies agree with the human Hi-C data. We conclude that the topological complexity of the human genome cannot be inferred from current Hi-C data.