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X-ray and computed tomography (CT) scanning technologies for COVID-19 screening have gained significant traction in AI research since the start of the coronavirus pandemic. Despite these continuous advancements for COVID-19 screening, many…
With the spread of COVID-19 over the world, the need arose for fast and precise automatic triage mechanisms to decelerate the spread of the disease by reducing human efforts e.g. for image-based diagnosis. Although the literature has shown…
In this paper, we explore how to use topological tools to compare dimension reduction methods. We first make a brief overview of some of the methods often used dimension reduction such as Isometric Feature Mapping, Laplacian Eigenmaps, Fast…
Understanding the protein folding process is an outstanding issue in biophysics; recent developments in molecular dynamics simulation have provided insights into this phenomenon. However, the large freedom of atomic motion hinders the…
During the outbreak time of COVID-19, computed tomography (CT) is a useful manner for diagnosing COVID-19 patients. Due to privacy issues, publicly available COVID-19 CT datasets are highly difficult to obtain, which hinders the research…
This paper is second in the series, following Pranav et al. (2019), focused on the characterization of geometric and topological properties of 3D Gaussian random fields. We focus on the formalism of persistent homology, the mainstay of…
Topological data analysis provides a set of tools to uncover low-dimensional structure in noisy point clouds. Prominent amongst the tools is persistence homology, which summarizes birth-death times of homological features using data objects…
Effective visualizations were evaluated to reveal relevant health patterns from multi-sensor real-time wearable devices that recorded vital signs from patients admitted to hospital with COVID-19. Furthermore, specific challenges associated…
A number of models in mathematical epidemiology have been developed to account for control measures such as vaccination or quarantine. However, COVID-19 has brought unprecedented social distancing measures, with a challenge on how to…
Developing reliable methods to discriminate different transient brain states that change over time is a key neuroscientific challenge in brain imaging studies. Topological data analysis (TDA), a novel framework based on algebraic topology,…
Persistent homology (PH) has been widely applied to graph data to extract topological features. However, little attention has been paid to how different distance functions on a graph affect the resulting persistence barcodes and their…
COVID-19 has caused thousands of deaths around the world and also resulted in a large international economic disruption. Identifying the pathways associated with this illness can help medical researchers to better understand the properties…
Cardiac digital twins (CDTs) of human cardiac electrophysiology (EP) are digital replicas of patient hearts that match like-for-like clinical observations. The electrocardiogram (ECG), as the most prevalent non-invasive observation of…
Introduction: During the COVID-19 pandemic, computed tomography (CT) was a popular method for diagnosing COVID-19 patients. HRCT (High-Resolution Computed Tomography) is a form of computed tomography that uses advanced methods to improve…
Despite the remarkable accuracies attained by machine learning classifiers to separate complex datasets in a supervised fashion, most of their operation falls short to provide an informed intuition about the structure of data, and, what is…
Persistent homology probes topological properties from point clouds and functions. By looking at multiple scales simultaneously, one can record the births and deaths of topological features as the scale varies. In this paper we use a…
The main purpose of this study is to develop a pipeline for COVID-19 detection from a big and challenging database of Computed Tomography (CT) images. The proposed pipeline includes a segmentation part, a lung extraction part, and a…
Asymptotic properties of statistical estimators play a significant role both in practice and in theory. However, many asymptotic results in statistics rely heavily on the independent and identically distributed (iid) assumption, which is…
In this paper, we present a new approach for analyzing gene expression data that builds on topological characteristics of time series. Our goal is to identify cell cycle regulated genes in micro array dataset. We construct a point cloud out…
We apply persistent homology, the main method in topological data analysis, to the study of demographic data. Persistence diagrams efficiently summarize information about clusters or peaks in a region's demographic data. To illustrate how…