🍩 Database of Original & Non-Theoretical Uses of Topology

(found 5 matches in 0.001231s)

  1. Visualizing Nanoparticle Surface Dynamics and Instabilities Enabled by Deep Denoising (2025)

    Peter A. Crozier, Matan Leibovich, Piyush Haluai, Mai Tan, Andrew M. Thomas, Joshua Vincent, Sreyas Mohan, Adria Marcos Morales, Shreyas A. Kulkarni, David S. Matteson, Yifan Wang, Carlos Fernandez-Granda
    Abstract Materials functionalities may be associated with atomic-level structural dynamics occurring on the millisecond timescale. However, the capability of electron microscopy to image structures with high spatial resolution and millisecond temporal resolution is often limited by poor signal-to-noise ratios. With an unsupervised deep denoising framework, we observed metal nanoparticle surfaces (platinum nanoparticles on cerium oxide) in a gas environment with time resolutions down to 10 milliseconds at a moderate electron dose. On this timescale, many nanoparticle surfaces continuously transition between ordered and disordered configurations. Stress fields can penetrate below the surface, leading to defect formation and destabilization, thus making the nanoparticle fluxional. Combining this unsupervised denoiser with in situ electron microscopy greatly improves spatiotemporal characterization, opening a new window for the exploration of atomic-level structural dynamics in materials.

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  2. Feature Detection and Hypothesis Testing for Extremely Noisy Nanoparticle Images Using Topological Data Analysis (2023)

    Andrew M. Thomas, Peter A. Crozier, Yuchen Xu, David S. Matteson
    Abstract We propose a flexible algorithm for feature detection and hypothesis testing in images with ultra-low signal-to-noise ratio using cubical persistent homology. Our main application is in the identification of atomic columns and other features in Transmission Electron Microscopy (TEM). Cubical persistent homology is used to identify local minima and their size in subregions in the frames of nanoparticle videos, which are hypothesized to correspond to relevant atomic features. We compare the performance of our algorithm to other employed methods for the detection of columns and their intensity. Additionally, Monte Carlo goodness-of-fit testing using real-valued summaries of persistence diagrams derived from smoothed images (generated from pixels residing in the vacuum region of an image) is developed and employed to identify whether or not the proposed atomic features generated by our algorithm are due to noise. Using these summaries derived from the generated persistence diagrams, one can produce univariate time series for the nanoparticle videos, thus, providing a means for assessing fluxional behavior. A guarantee on the false discovery rate for multiple Monte Carlo testing of identical hypotheses is also established.

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  4. 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.

  5. Ghrist Barcoded Video Frames. Application in Detecting Persistent Visual Scene Surface Shapes Captured in Videos (2019)

    Arjuna P. H. Don, James F. Peters
    Abstract This article introduces an application of Ghrist barcodes in the study of persistent Betti numbers derived from vortex nerve complexes found in triangulations of video frames. A Ghrist barcode (also called a persistence barcode) is a topology of data pic- tograph useful in representing the persistence of the features of changing shapes. The basic approach is to introduce a free Abelian group representation of intersecting filled polygons on the barycenters of the triangles of Alexandroff nerves. An Alexandroff nerve is a maximal collection of triangles of a common vertex in the triangulation of a finite, bounded planar region. In our case, the planar region is a video frame. A Betti number is a count of the number of generators is a finite Abelian group. The focus here is on the persistent Betti numbers across sequences of triangulated video frames. Each Betti number is mapped to an entry in a Ghrist barcode. Two main results are given, namely, vortex nerves are Edelsbrunner-Harer nerve complexes and the Betti number of a vortex nerve equals k + 2 for a vortex nerve containing k edges attached between a pair of vortex cycles in the nerve.