Persistent homology
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Hierarchical structures of amorphous solids characterized by persistent homology Open
Significance Persistent homology is an emerging mathematical concept for characterizing shapes of data. In particular, it provides a tool called the persistence diagram that extracts multiscale topological features such as rings and caviti…
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TopologyNet: Topology based deep convolutional and multi-task neural networks for biomolecular property predictions Open
weilab.math.msu.edu/TDL/.
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Persistent homology analysis of brain artery trees Open
New representations of tree-structured data objects, using ideas from topological data analysis, enable improved statistical analyses of a population of brain artery trees. A number of representations of each data tree arise from persisten…
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Quantum algorithms for topological and geometric analysis of data Open
Extracting useful information from large data sets can be a daunting task. Topological methods for analysing data sets provide a powerful technique for extracting such information. Persistent homology is a sophisticated tool for identifyin…
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A Topological Loss Function for Deep-Learning Based Image Segmentation Using Persistent Homology Open
We introduce a method for training neural networks to perform image or volume segmentation in which prior knowledge about the topology of the segmented object can be explicitly provided and then incorporated into the training process. By u…
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Ripser.py: A Lean Persistent Homology Library for Python Open
by computing topological descriptors that summarize features as connected components, loops, and voids.TDA has found wide applications across nonlinear time series analysis (Perea & Harer, 2015), com
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Topological Data Analysis of Biological Aggregation Models Open
We apply tools from topological data analysis to two mathematical models inspired by biological aggregations such as bird flocks, fish schools, and insect swarms. Our data consists of numerical simulation output from the models of Vicsek a…
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Deep Residual Learning for Compressed Sensing CT Reconstruction via Persistent Homology Analysis Open
Recently, compressed sensing (CS) computed tomography (CT) using sparse projection views has been extensively investigated to reduce the potential risk of radiation to patient. However, due to the insufficient number of projection views, a…
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Persistence Images: A Stable Vector Representation of Persistent Homology Open
Many datasets can be viewed as a noisy sampling of an underlying space, and tools from topological data analysis can characterize this structure for the purpose of knowledge discovery. One such tool is persistent homology, which provides a…
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Persistent homology of time-dependent functional networks constructed from coupled time series Open
We use topological data analysis to study “functional networks” that we construct from time-series data from both experimental and synthetic sources. We use persistent homology with a weight rank clique filtration to gain insights into the…
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Localization in the Crowd with Topological Constraints Open
We address the problem of crowd localization, i.e., the prediction of dots corresponding to people in a crowded scene. Due to various challenges, a localization method is prone to spatial semantic errors, i.e., predicting multiple dots wit…
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Persistent Homology Analysis for Materials Research and Persistent Homology Software: HomCloud Open
This paper introduces persistent homology, which is a powerful tool to\ncharacterize the shape of data using the mathematical concept of topology. We\nexplain the fundamental idea of persistent homology from scratch using some\nexamples. W…
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Analysis and prediction of protein folding energy changes upon mutation by element specific persistent homology Open
Supplementary data are available at Bioinformatics online.
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Persistent spectral graph Open
Persistent homology is constrained to purely topological persistence, while multiscale graphs account only for geometric information. This work introduces persistent spectral theory to create a unified low‐dimensional multiscale paradigm f…
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Edge Collapse and Persistence of Flag Complexes Open
In this article, we extend the notions of dominated vertex and strong collapse of a simplicial complex as introduced by J. Barmak and E. Miniam. We say that a simplex (of any dimension) is dominated if its link is a simplicial cone. Domina…
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Deep Learning with Topological Signatures Open
Inferring topological and geometrical information from data can offer an alternative perspective on machine learning problems. Methods from topological data analysis, e.g., persistent homology, enable us to obtain such information, typical…
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Geometric and Topological Inference Open
Geometric and topological inference deals with the retrieval of information about a geometric object using only a finite set of possibly noisy sample points. It has connections to manifold learning and provides the mathematical and algorit…
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A topological approach for proteinclassification Open
Protein function and dynamics are closely related to its sequence and structure.However, prediction of protein function and dynamics from its sequence and structure is still a fundamental challenge in molecular biology. Protein classificat…
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Persistent homology of complex networks for dynamic state detection Open
In this paper we develop an alternative topological data analysis (TDA) approach for studying graph representations of time series of dynamical systems. Specifically, we show how persistent homology, a tool from TDA, can be used to yield a…
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Persistent Homology for the Quantitative Evaluation of Architectural Features in Prostate Cancer Histology Open
The current system for evaluating prostate cancer architecture is the Gleason grading system which divides the morphology of cancer into five distinct architectural patterns, labeled 1 to 5 in increasing levels of cancer aggressiveness, an…
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Topological representations of crystalline compounds for the machine-learning prediction of materials properties Open
Accurate theoretical predictions of desired properties of materials play an important role in materials research and development. Machine learning (ML) can accelerate the materials design by building a model from input data. For complex da…
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Multiparameter persistent homology landscapes identify immune cell spatial patterns in tumors Open
Significance Quantifying and comparing complex spatial biological datasets is crucial for medical applications and remains an active area of research. As datasets become more heterogeneous and complicated, so must the methods that are used…
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Morse complexes for shape segmentation and homological analysis: discrete models and algorithms Open
Morse theory offers a natural and mathematically‐sound tool for shape analysis and understanding. It allows studying the behavior of a scalar function defined on a manifold. Starting from a Morse function, we can decompose the domain of th…
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PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures Open
Persistence diagrams, the most common descriptors of Topological Data Analysis, encode topological properties of data and have already proved pivotal in many different applications of data science. However, since the (metric) space of pers…
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Metrics for comparing neuronal tree shapes based on persistent homology Open
As more and more neuroanatomical data are made available through efforts such as NeuroMorpho.Org and FlyCircuit.org, the need to develop computational tools to facilitate automatic knowledge discovery from such large datasets becomes more …
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Topological Data Analysis as a Morphometric Method: Using Persistent Homology to Demarcate a Leaf Morphospace Open
Current morphometric methods that comprehensively measure shape cannot compare the disparate leaf shapes found in seed plants and are sensitive to processing artifacts. We explore the use of persistent homology, a topological method applie…
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Persistent homology analysis of craze formation Open
We apply a persistent homology analysis to investigate the behavior of nanovoids during the crazing process of glassy polymers. We carry out a coarse-grained molecular dynamics simulation of the uniaxial deformation of an amorphous polymer…
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Principal component analysis of persistent homology rank functions with case studies of spatial point patterns, sphere packing and colloids Open
Persistent homology, while ostensibly measuring changes in topology, captures\nmultiscale geometrical information. It is a natural tool for the analysis of\npoint patterns. In this paper we explore the statistical power of the\n(persistent…
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Algebraic stability of zigzag persistence modules Open
The stability theorem for persistent homology is a central result in topological data analysis. While the original formulation of the result concerns the persistence barcodes of [math] –valued functions, the result was later cast in a more…
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Topological Persistence for Relating Microstructure and Capillary Fluid Trapping in Sandstones Open
Results from a series of two‐phase fluid flow experiments in Leopard, Berea, and Bentheimer sandstones are presented. Fluid configurations are characterized using laboratory‐based and synchrotron based 3‐D X‐ray computed tomography. All fl…