Related papers: Topological feature study of slope failure process…
We propose a study of multipartite entanglement through persistent homology, a tool used in topological data analysis. In persistent homology, a 1-parameter filtration of simplicial complexes called persistence complex is used to reveal…
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 lifetime of…
Recently a new feature representation and data analysis methodology based on a topological tool called persistent homology (and its corresponding persistence diagram summary) has started to attract momentum. A series of methods have been…
Persistent Homology is a widely used topological data analysis tool that creates a concise description of the topological properties of a point cloud based on a specified filtration. Most filtrations used for persistent homology depend…
Software reliability models are an important tool in quality management and release planning. There is a large number of different models that often exhibit strengths in different areas. This paper proposes a model that is based on a…
Convection is a well-studied topic in fluid dynamics, yet it is less understood in the context of networks flows. Here, we incorporate techniques from topological data analysis (namely, persistent homology) to automate the detection and…
Persistent homology captures the evolution of topological features of a model as a parameter changes. The most commonly used summary statistics of persistent homology are the barcode and the persistence diagram. Another summary statistic,…
Topological correctness is critical for segmentation of tubular structures, which pervade in biomedical images. Existing topological segmentation loss functions are primarily based on the persistent homology of the image. They match the…
Although image denoising algorithms have attracted significant research attention, surprisingly few have been proposed for, or evaluated on, noise from imagery acquired under real low-light conditions. Moreover, noise characteristics are…
In this paper we develop a novel 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…
Topological data analysis and its main method, persistent homology, provide a toolkit for computing topological information of high-dimensional and noisy data sets. Kernels for one-parameter persistent homology have been established to…
Solving optimization tasks based on functions and losses with a topological flavor is a very active, growing field of research in data science and Topological Data Analysis, with applications in non-convex optimization, statistics and…
This paper introduces an unsupervised method to estimate the class separability of text datasets from a topological point of view. Using persistent homology, we demonstrate how tracking the evolution of embedding manifolds during training…
In recent years there has been noticeable interest in the study of the "shape of data". Among the many ways a "shape" could be defined, topology is the most general one, as it describes an object in terms of its connectivity structure:…
We use methods from topological data analysis to study the topological features of certain distributions of string vacua. Topological data analysis is a multi-scale approach used to analyze the topological features of a dataset by…
Modern representation learning increasingly relies on unsupervised and self-supervised methods trained on large-scale unlabeled data. While these approaches achieve impressive generalization across tasks and domains, evaluating embedding…
Interacting, self-propelled particles such as epithelial cells can dynamically self-organize into complex multicellular patterns, which are challenging to classify without a priori information. Classically, different phases and phase…
To analyze the topological properties of the given discrete data, one needs to consider a continuous transform called filtration. Persistent homology serves as a tool to track changes of homology in the filtration. The outcome of the…
We apply modern methods in computational topology to the task of discovering and characterizing phase transitions. As illustrations, we apply our method to four two-dimensional lattice spin models: the Ising, square ice, XY, and…
Persistent Homology is a fairly new branch of Computational Topology which combines geometry and topology for an effective shape description of use in Pattern Recognition. In particular it registers through "Betti Numbers" the presence of…