🍩 Database of Original & Non-Theoretical Uses of Topology

(found 6 matches in 0.00217s)
  1. 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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  2. Severe Slugging Flow Identification From Topological Indicators (2022)

    Simone Casolo
    Abstract In this work, topological data analysis is used to identify the onset of severe slug flow in offshore petroleum production systems. Severe slugging is a multiphase flow regime known to be very inefficient and potentially harmful to process equipment and it is characterized by large oscillations in the production fluid pressure. Time series from pressure sensors in subsea oil wells are processed by means of Takens embedding to produce point clouds of data. Embedded sensor data is then analyzed using persistent homology to obtain topological indicators capable of revealing the occurrence of severe slugging in a condition-based monitoring approach. A large dataset of well events consisting of both real and simulated data is used to demonstrate the possibilty of authomatizing severe slugging detection from live data via topological data analysis. Methods based on persistence diagrams are shown to accurately identify severe slugging and to classify different flow regimes from pressure signals of producing wells with supervised machine learning.
  3. Emotion Recognition in Talking-Face Videos Using Persistent Entropy and Neural Networks (2022)

    Eduardo Paluzo-Hidalgo, Rocio Gonzalez-Diaz, Guillermo Aguirre-Carrazana, Eduardo Paluzo-Hidalgo, Rocio Gonzalez-Diaz, Guillermo Aguirre-Carrazana
    Abstract \textlessabstract\textgreater\textlessp\textgreaterThe automatic recognition of a person's emotional state has become a very active research field that involves scientists specialized in different areas such as artificial intelligence, computer vision, or psychology, among others. Our main objective in this work is to develop a novel approach, using persistent entropy and neural networks as main tools, to recognise and classify emotions from talking-face videos. Specifically, we combine audio-signal and image-sequence information to compute a \textlessitalic\textgreatertopology signature\textless/italic\textgreater (a 9-dimensional vector) for each video. We prove that small changes in the video produce small changes in the signature, ensuring the stability of the method. These topological signatures are used to feed a neural network to distinguish between the following emotions: calm, happy, sad, angry, fearful, disgust, and surprised. The results reached are promising and competitive, beating the performances achieved in other state-of-the-art works found in the literature.\textless/p\textgreater\textless/abstract\textgreater
  4. Stable Topological Summaries for Analyzing the Organization of Cells in a Packed Tissue (2021)

    Nieves Atienza, Maria-Jose Jimenez, Manuel Soriano-Trigueros
    Abstract We use topological data analysis tools for studying the inner organization of cells in segmented images of epithelial tissues. More specifically, for each segmented image, we compute different persistence barcodes, which codify the lifetime of homology classes (persistent homology) along different filtrations (increasing nested sequences of simplicial complexes) that are built from the regions representing the cells in the tissue. We use a complete and well-grounded set of numerical variables over those persistence barcodes, also known as topological summaries. A novel combination of normalization methods for both the set of input segmented images and the produced barcodes allows for the proven stability results for those variables with respect to small changes in the input, as well as invariance to image scale. Our study provides new insights to this problem, such as a possible novel indicator for the development of the drosophila wing disc tissue or the importance of centroids’ distribution to differentiate some tissues from their CVT-path counterpart (a mathematical model of epithelia based on Voronoi diagrams). We also show how the use of topological summaries may improve the classification accuracy of epithelial images using a Random Forest algorithm.
  5. Characterising Epithelial Tissues Using Persistent Entropy (2019)

    N. Atienza, L. M. Escudero, M. J. Jimenez, M. Soriano-Trigueros
    Abstract In this paper, we apply persistent entropy, a novel topological statistic, for characterization of images of epithelial tissues. We have found out that persistent entropy is able to summarize topological and geometric information encoded by \$\$\alpha \$\$α-complexes and persistent homology. After using some statistical tests, we can guarantee the existence of significant differences in the studied tissues.
  6. Persistent Homology Analysis of Osmolyte Molecular Aggregation and Their Hydrogen-Bonding Networks (2019)

    Kelin Xia, D. Vijay Anand, Saxena Shikhar, Yuguang Mu
    Abstract Dramatically different properties have been observed for two types of osmolytes, i.e., trimethylamine N-oxide (TMAO) and urea, in a protein folding process. Great progress has been made in revealing the potential underlying mechanism of these two osmolyte systems. However, many problems still remain unsolved. In this paper, we propose to use the persistent homology to systematically study the osmolytes’ molecular aggregation and their hydrogen-bonding network from a global topological perspective. It has been found that, for the first time, TMAO and urea show two extremely different topological behaviors, i.e., an extensive network and local clusters, respectively. In general, TMAO forms highly consistent large loop or circle structures in high concentrations. In contrast, urea is more tightly aggregated locally. Moreover, the resulting hydrogen-bonding networks also demonstrate distinguishable features. With a concentration increase, TMAO hydrogen-bonding networks vary greatly in their total number of loop structures and large-sized loop structures consistently increase. In contrast, urea hydrogen-bonding networks remain relatively stable with slight reduction of the total loop number. Moreover, the persistent entropy (PE) is, for the first time, used in characterization of the topological information of the aggregation and hydrogen-bonding networks. The average PE systematically increases with the concentration for both TMAO and urea, and decreases in their hydrogen-bonding networks. But their PE variances have totally different behaviors. Finally, topological features of the hydrogen-bonding networks are found to be highly consistent with those from the ion aggregation systems, indicating that our topological invariants can characterize intrinsic features of the “structure making” and “structure breaking” systems.