scholarly journals Persistent Homology: Application To Monitoring Hydraulic Fracturing

2020 ◽  
Vol 23 (6) ◽  
pp. 1192-1212
Author(s):  
Kirill Yurevich Erofeev ◽  
Mansur Tagirovich Ziiatdinov ◽  
Evgenii Vladimirovich Mokshin
Keyword(s):  
Data Analysis ◽  
Hydraulic Fracturing ◽  
Topological Structure ◽  
Prior Information ◽  
Persistent Homology ◽  
Topological Data Analysis ◽  
Analysis Tool ◽  
Data Analysis Tool ◽  
Natural Way ◽  
Topological Data

Persistent homology is a topological data analysis tool which is reflecting changes in topological structure of data along its scale. Application of persistent homology to monitoring hydraulic fracturing which is allowing researchers to consider prior information in a natural way is given in the article

scholarly journals Persistent Homology Analysis of RNA

2016 ◽  
Vol 4 (1) ◽  
Author(s):  
Adane L. Mamuye ◽  
Matteo Rucco ◽  
Luca Tesei ◽  
Emanuela Merelli
Keyword(s):  
Data Analysis ◽  
Rna Folding ◽  
Persistent Homology ◽  
Betti Numbers ◽  
Structural Features ◽  
Topological Data Analysis ◽  
Analysis Tool ◽  
Global Features ◽  
Folding Space ◽  
Topological Data

AbstractTopological data analysis has been recently used to extract meaningful information frombiomolecules. Here we introduce the application of persistent homology, a topological data analysis tool, for computing persistent features (loops) of the RNA folding space. The scaffold of the RNA folding space is a complex graph from which the global features are extracted by completing the graph to a simplicial complex via the notion of clique and Vietoris-Rips complexes. The resulting simplicial complexes are characterised in terms of topological invariants, such as the number of holes in any dimension, i.e. Betti numbers. Our approach discovers persistent structural features, which are the set of smallest components to which the RNA folding space can be reduced. Thanks to this discovery, which in terms of data mining can be considered as a space dimension reduction, it is possible to extract a new insight that is crucial for understanding the mechanism of the RNA folding towards the optimal secondary structure. This structure is composed by the components discovered during the reduction step of the RNA folding space and is characterized by minimum free energy.

scholarly journals Classification of apatite structures via topological data analysis: a framework for a ‘Materials Barcode’ representation of structure maps

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Scott Broderick ◽  
Ruhil Dongol ◽  
Tianmu Zhang ◽  
Krishna Rajan
Keyword(s):  
Machine Learning ◽  
Data Analysis ◽  
Crystal Chemistry ◽  
Persistent Homology ◽  
Hierarchical Classification ◽  
Topological Data Analysis ◽  
Learning Tool ◽  
Coordination Polyhedra ◽  
Machine Learning Tool ◽  
Topological Data

AbstractThis paper introduces the use of topological data analysis (TDA) as an unsupervised machine learning tool to uncover classification criteria in complex inorganic crystal chemistries. Using the apatite chemistry as a template, we track through the use of persistent homology the topological connectivity of input crystal chemistry descriptors on defining similarity between different stoichiometries of apatites. It is shown that TDA automatically identifies a hierarchical classification scheme within apatites based on the commonality of the number of discrete coordination polyhedra that constitute the structural building units common among the compounds. This information is presented in the form of a visualization scheme of a barcode of homology classifications, where the persistence of similarity between compounds is tracked. Unlike traditional perspectives of structure maps, this new “Materials Barcode” schema serves as an automated exploratory machine learning tool that can uncover structural associations from crystal chemistry databases, as well as to achieve a more nuanced insight into what defines similarity among homologous compounds.

scholarly journals Topological data analysis for true step detection in periodic piecewise constant signals

2018 ◽  
Vol 474 (2218) ◽  
pp. 20180027 ◽  
Author(s):  
Firas A. Khasawneh ◽  
Elizabeth Munch
Keyword(s):  
Data Analysis ◽  
Persistent Homology ◽  
Topological Data Analysis ◽  
Future Research ◽  
Accurate Identification ◽  
Piecewise Constant ◽  
Higher Dimensional ◽  
Powerful Approach ◽  
Hadamard Transforms ◽  
Topological Data

This paper introduces a simple yet powerful approach based on topological data analysis for detecting true steps in a periodic, piecewise constant (PWC) signal. The signal is a two-state square wave with randomly varying in-between-pulse spacing, subject to spurious steps at the rising or falling edges which we call digital ringing. We use persistent homology to derive mathematical guarantees for the resulting change detection which enables accurate identification and counting of the true pulses. The approach is tested using both synthetic and experimental data obtained using an engine lathe instrumented with a laser tachometer. The described algorithm enables accurate and automatic calculations of the spindle speed without any choice of parameters. The results are compared with the frequency and sequency methods of the Fourier and Walsh–Hadamard transforms, respectively. Both our approach and the Fourier analysis yield comparable results for pulses with regular spacing and digital ringing while the latter causes large errors using the Walsh–Hadamard method. Further, the described approach significantly outperforms the frequency/sequency analyses when the spacing between the peaks is varied. We discuss generalizing the approach to higher dimensional PWC signals, although using this extension remains an interesting question for future research.

scholarly journals Topological Data Analysis as a Morphometric Method: Using Persistent Homology to Demarcate a Leaf Morphospace

2018 ◽  
Vol 9 ◽  
Author(s):  
Mao Li ◽  
Hong An ◽  
Ruthie Angelovici ◽  
Clement Bagaza ◽  
Albert Batushansky ◽  
...  
Keyword(s):  
Data Analysis ◽  
Persistent Homology ◽  
Topological Data Analysis ◽  
Morphometric Method ◽  
Topological Data

scholarly journals Persistent homology as a new method of the assessment of heart rate variability

PLoS ONE ◽  
2021 ◽  
Vol 16 (7) ◽  
pp. e0253851
Author(s):  
Grzegorz Graff ◽  
Beata Graff ◽  
Paweł Pilarczyk ◽  
Grzegorz Jabłoński ◽  
Dariusz Gąsecki ◽  
...  
Keyword(s):  
Heart Rate ◽  
Heart Rate Variability ◽  
Data Analysis ◽  
Persistent Homology ◽  
Assessment Tools ◽  
Topological Data Analysis ◽  
Topological Descriptors ◽  
Time Interval ◽  
Analysis Tool ◽  
Frequency Domain Methods

Heart rate variability (hrv) is a physiological phenomenon of the variation in the length of the time interval between consecutive heartbeats. In many cases it could be an indicator of the development of pathological states. The classical approach to the analysis of hrv includes time domain methods and frequency domain methods. However, attempts are still being made to define new and more effective hrv assessment tools. Persistent homology is a novel data analysis tool developed in the recent decades that is rooted at algebraic topology. The Topological Data Analysis (TDA) approach focuses on examining the shape of the data in terms of connectedness and holes, and has recently proved to be very effective in various fields of research. In this paper we propose the use of persistent homology to the hrv analysis. We recall selected topological descriptors used in the literature and we introduce some new topological descriptors that reflect the specificity of hrv, and we discuss their relation to the standard hrv measures. In particular, we show that this novel approach provides a collection of indices that might be at least as useful as the classical parameters in differentiating between series of beat-to-beat intervals (RR-intervals) in healthy subjects and patients suffering from a stroke episode.

scholarly journals Flow Estimation Only from Image Data, based on Persistent Homology

2021 ◽  
Author(s):  
Anna Suzuki ◽  
Miyuki Miyazawa ◽  
James Minto ◽  
Takeshi Tsuji ◽  
Ippei Obayashi ◽  
...  
Keyword(s):  
Data Analysis ◽  
Persistent Homology ◽  
Image Data ◽  
Fracture Network ◽  
Topological Data Analysis ◽  
Geometric Information ◽  
Flow Estimation ◽  
Flow Phenomena ◽  
Network Patterns ◽  
Topological Data

Abstract Topological data analysis is an emerging concept of data analysis for characterizing shapes. A state-of-the-art tool in topological data analysis is persistent homology, which is expected to summarize quantified topological and geometric features. Although persistent homology is useful for revealing the topological and geometric information, it is difficult to interpret the parameters of persistent homology themselves and difficult to directly relate the parameters to physical properties. In this study, we focus on connectivity and apertures of flow channels detected from persistent homology analysis. We propose a method to estimate permeability in fracture networks from parameters of persistent homology. Synthetic 3D fracture network patterns and their direct flow simulations are used for the validation. The results suggest that the persistent homology can estimate fluid flow in fracture network based on the image data. This method can easily derive the flow phenomena based on the information of the structure.

scholarly journals Using Topological Data Analysis (TDA) and Persistent Homology to Analyze the Stock Markets in Singapore and Taiwan

2021 ◽  
Vol 9 ◽  
Author(s):  
Peter Tsung-Wen Yen ◽  
Siew Ann Cheong
Keyword(s):  
Data Analysis ◽  
Stock Markets ◽  
Persistent Homology ◽  
Betti Numbers ◽  
Stock Index ◽  
Topological Data Analysis ◽  
Series Data ◽  
Topological Features ◽  
Market Crashes ◽  
Topological Data

In recent years, persistent homology (PH) and topological data analysis (TDA) have gained increasing attention in the fields of shape recognition, image analysis, data analysis, machine learning, computer vision, computational biology, brain functional networks, financial networks, haze detection, etc. In this article, we will focus on stock markets and demonstrate how TDA can be useful in this regard. We first explain signatures that can be detected using TDA, for three toy models of topological changes. We then showed how to go beyond network concepts like nodes (0-simplex) and links (1-simplex), and the standard minimal spanning tree or planar maximally filtered graph picture of the cross correlations in stock markets, to work with faces (2-simplex) or any k-dim simplex in TDA. By scanning through a full range of correlation thresholds in a procedure called filtration, we were able to examine robust topological features (i.e. less susceptible to random noise) in higher dimensions. To demonstrate the advantages of TDA, we collected time-series data from the Straits Times Index and Taiwan Capitalization Weighted Stock Index (TAIEX), and then computed barcodes, persistence diagrams, persistent entropy, the bottleneck distance, Betti numbers, and Euler characteristic. We found that during the periods of market crashes, the homology groups become less persistent as we vary the characteristic correlation. For both markets, we found consistent signatures associated with market crashes in the Betti numbers, Euler characteristics, and persistent entropy, in agreement with our theoretical expectations.

scholarly journals Persistent homology approach distinguishes potential pattern between “Early” and “Not Early” hepatic decompensation groups using MRI modalities

2021 ◽  
Vol 7 (2) ◽  
pp. 488-491
Author(s):  
Yashbir Singh ◽  
William Jons ◽  
Gian Marco Conte ◽  
Jaidip Jagtap ◽  
Kuan Zhang ◽  
...  
Keyword(s):  
Data Analysis ◽  
Liver Failure ◽  
Algebraic Topology ◽  
Persistent Homology ◽  
Topological Data Analysis ◽  
Topological Representation ◽  
Hepatic Decompensation ◽  
Topological Data

Abstract Primary sclerosis cholangitis (PSC) predisposes individuals to liver failure, but it is challenging for radiologists examining radiologic images to predict which patients with PSC will ultimately develop liver failure. Motivated by algebraic topology, a topological data analysis - inspired framework was adopted in the study of the imaging pattern between the “Early Decompensation” and “Not Early” groups. The results demonstrate that the proposed methodology discriminates “Early Decompensation” and “Not Early” groups. Our study is the first attempt to provide a topological representation-based method into early hepatic decompensation and not early groups.

scholarly journals Revealing hidden medium-range order in amorphous materials using topological data analysis

2020 ◽  
Vol 6 (37) ◽  
pp. eabc2320
Author(s):  
Søren S. Sørensen ◽  
Christophe A. N. Biscio ◽  
Mathieu Bauchy ◽  
Lisbeth Fajstrup ◽  
Morten M. Smedskjaer
Keyword(s):  
Data Analysis ◽  
Amorphous Materials ◽  
Persistent Homology ◽  
Amorphous Solids ◽  
Range Order ◽  
Silicate Glasses ◽  
Topological Data Analysis ◽  
Medium Range Order ◽  
Medium Range ◽  
Topological Data

Despite the numerous technological applications of amorphous materials, such as glasses, the understanding of their medium-range order (MRO) structure—and particularly the origin of the first sharp diffraction peak (FSDP) in the structure factor—remains elusive. Here, we use persistent homology, an emergent type of topological data analysis, to understand MRO structure in sodium silicate glasses. To enable this analysis, we introduce a self-consistent categorization of rings with rigorous geometrical definitions of the structural entities. Furthermore, we enable quantitative comparison of the persistence diagrams by computing the cumulative sum of all points weighted by their lifetime. On the basis of these analysis methods, we show that the approach can be used to deconvolute the contributions of various MRO features to the FSDP. More generally, the developed methodology can be applied to analyze and categorize molecular dynamics data and understand MRO structure in any class of amorphous solids.

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