Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 17 of 17 for “"persistent homology"”.
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Quantifying wildlife diversity using persistent homology
Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2024-12-01
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Structural features of persistent homology and their algorithmic transformations
… and orthodox methods that underlie the study of persistent homology, particularly in its calculation of homological cycle representatives that are associated to persistence diagrams. A common background to the subject covers several aspects: schemes to process input data (embedding it in a …
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Plumbing the Depths of the Shallow End: Exploring Persistent Homology Using Small Data
<p>Persistent homology is a prominent tool in topological data analysis. This thesis is designed to be an introduction and guide to a beginner in persistent homology. This comprehensive overview discusses the math used behind it, the code needed to apply it, and its current place in the field. We …
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Using Persistent Homology for Topological Analysis of Protein Interaction Network of Candida Antarctica Lipase B Molecular Dynamic Simulation Model
… network from a broader perspective. The ”Persistent Homol- ogy (PH) method” is then presented as a way to exceed pairwise interactions and examine protein networks in terms of patterns of interaction between the nodes. Per- sistent Homology studies the evolution of the protein interaction …
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Decomposition of Certain Representations Into A Direct Sum of Indecomposable Representations
… of quivers and posets are produced by persistent homology. It is possible to decompose such representations into direct sums of indecomposable representations. The indecomposable representations of quivers and posets that arise from one dimensional persistent homology are well …
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Topics in applied topology
Persistent homology has emerged as a powerful tool in Topological Data Analysis (TDA) for extracting structural information from complex datasets by tracking topological features across varying scales. While 1-parameter persistent homology offers a mature theory with well-defined invariants like …
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Patterns in dynamics
… this paper we introduce and explore the idea of persistent homology (PH) and discuss several applications of this computational topology tool beyond its intended purpose. In particular we apply persistence to data generated by dynamical systems. The application of persistent homology to the …
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Generalized Rank Invariant : Structure, Möbius Inversion, and Persistence Diagram
Topological Data Analysis relies on persistent homology to quantify the shape of data. Unlike the one-parameter case, multiparameter persistence modules lack a complete discrete invariant analogous to barcodes, and their classification requires tools that can capture subtle interactions across the …
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Homological Illusions of Persistence and Stability
… this thesis we explore and extend the theory of persistent homology, which captures topological features of a function by pairing its critical values. The result is represented by a collection of points in the extended plane called persistence diagram.</p><p>We start with the question of ridding …
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Topology of Social and Managerial Networks
… methods for network analysis relying on persistent homology. The results gained by the new methods apply both to weighted and unweighted networks; showing that classi- cal connectivity measures on managerial and societal networks can be very imprecise and extending them to weighted …
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Investigating the Relationships Between Disorder, Structure, and Dynamics in Amorphous Systems
… deformations, and we develop an extension of persistent homology to isolate these bursts of localized deformations. Further, we extend existing tools for the structural evaluation of mechanically stable systems to generically unstable systems to identify how soft regions evolve and change …
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Shape Reconstruction with Topological Priors
… 2D, and 3D cases:</p><p>In 1D, we show that the persistent extrema of the curvature function of a closed curve are useful for shape simplication. In 2D, we study how to label a scene into multiple tiers to approximate the actual scene layout. We use the number of extrema as a topological prior to …
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Applied topology through the lens of Analytic Combinatorics
Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2025-05-01
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Evolutionary Ecology of the First Animal Ecosystems
… methodologies, including surface metrology, persistent homology and discrete phase modelling, which promise to have wide-ranging future applications both the field of early animal evolution and palaeobiology more generally. I uncover several important ecological processes operating in these …
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Exploring topological data analysis in gene expression data topology-driven biomarker discovery and clinical outcome prediction in oncology
… we position Topological Data Analysis (TDA) and persistent homology at the core of a novel analytical framework designed to tackle two key challenges in cancer research: clinical outcome prediction and biomarker discovery. In this study, we employ Weighted Gene Topological Data Analysis (WGTDA) …
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Combining Chemometrics and non-target GC-IMS gas phase analysis for improved bioprocess monitoring
… was to extract peak lists from the raw data. Persistent homology was proposed as a suitable algorithm for automated peak detection in two-dimensional GC-IMS data. Its performance was evaluated on two publicly available datasets with different GC setups, peak shapes, and resolution. The …