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Cell biologists study in parallel the morphology of cells with the regulation mechanisms that modify this morphology. Such studies are complicated by the inherent heterogeneity present in the cell population. It remains difficult to define…

Topological Data Analysis is a relatively new field of study that uses topological invariants to study the shape of data. We analyze a dataset provided by the Centers for Disease Control and Prevention (CDC) using persistent homology and…

We develop a method for analyzing spatial and spatiotemporal anomalies in geospatial data using topological data analysis (TDA). To do this, we use persistent homology (PH), which allows one to algorithmically detect geometric voids in a…

Persistent Homology is a powerful tool in Topological Data Analysis (TDA) to capture topological properties of data succinctly at different spatial resolutions. For graphical data, shape, and structure of the neighborhood of individual data…

Convolutional neural networks (CNNs) are a standard tool for computer vision tasks such as image classification. However, typical model architectures may result in the loss of topological information. In specific domains such as…

This article studies the robust version of persistent homology based on trimming methodology to capture the geometric feature through support of the data in presence of outliers. Precisely speaking, the proposed methodology works when the…

Topological data analysis is an approach to study shape of a data set by means of topology. Its main object of study is the persistence diagram, which represents the topological features of the data set at different spatial resolutions.…

Topological data analysis (TDA), while abstract, allows a characterization of time-series data obtained from nonlinear and complex dynamical systems. Though it is surprising that such an abstract measure of structure - counting pieces and…

Chest computed tomography (CT) has played an essential diagnostic role in assessing patients with COVID-19 by showing disease-specific image features such as ground-glass opacity and consolidation. Image segmentation methods have proven to…

Countries are recording health information on the global spread of COVID-19 using different methods, sometimes changing the rules after a few days. They are all publishing the number of new individuals infected, cured and dead, along with…

Gait recognition is an important biometric technique for video surveillance tasks, due to the advantage of using it at distance. In this paper, we present a persistent homology-based method to extract topological features (the so-called…

Accurate and interpretable brain tumor classification from medical imaging remains a challenging problem due to the high dimensionality and complex structural patterns present in magnetic resonance imaging (MRI). In this study, we propose a…

Introduction: For COVID-19 patients accurate prediction of disease severity and mortality risk would greatly improve care delivery and resource allocation. There are many patient-related factors, such as pre-existing comorbidities that…

X-ray images may present non-trivial features with predictive information of patients that develop severe symptoms of COVID-19. If true, this hypothesis may have practical value in allocating resources to particular patients while using a…

Topological Data Analysis (TDA) is an approach to handle with big data by studying its shape. A main tool of TDA is the persistence diagram, and one can use it to compare data sets. One approach to learn on the similarity between two…

Single-parameter persistent homology, a key tool in topological data analysis, has been widely applied to data problems along with statistical techniques that quantify the significance of the results. In contrast, statistical techniques for…

We characterize structures such as monotonicity, convexity, and modality in smooth regression curves using persistent homology. Persistent homology is a key tool in topological data analysis that detects higher-dimensional topological…

Visualization in the emerging field of topological data analysis has progressed from persistence barcodes and persistence diagrams to display of two-parameter persistent homology. Although persistence barcodes and diagrams have permitted…

Multiplexed imaging allows multiple cell types to be simultaneously visualised in a single tissue sample, generating unprecedented amounts of spatially-resolved, biological data. In topological data analysis, persistent homology provides…

Persistent homology is a common technique in topological data analysis providing geometrical and topological information about the sample space. All this information, known as topological features, is summarized in persistence diagrams, and…