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The machinery of topological data analysis becomes increasingly popular in a broad range of machine learning tasks, ranging from anomaly detection and manifold learning to graph classification. Persistent homology is one of the key…
Phase separation mechanisms can produce a variety of complicated and intricate microstructures, which often can be difficult to characterize in a quantitative way. In recent years, a number of novel topological metrics for microstructures…
An accurate assessment of the cardiovascular system and prediction of cardiovascular diseases (CVDs) are crucial. Measured cardiac blood flow data provide insights about patient-specific hemodynamics, where many specialized techniques have…
The current COVID-19 pandemic is a serious threat to humanity that directly affects the lungs. Automatic identification of COVID-19 is a challenge for health care officials. The standard gold method for diagnosing COVID-19 is Reverse…
The statistical mechanical approach to complex networks is the dominant paradigm in describing natural and societal complex systems. The study of network properties, and their implications on dynamical processes, mostly focus on locally…
The COVID-19 pandemic demonstrated that fast and accurate analysis of continually collected infectious disease surveillance data is crucial for situational awareness and policy making. Coalescent-based phylodynamic analysis can use genetic…
Recent advances in molecular and genetic research have identified a diverse range of brain tumor sub-types, shedding light on differences in their molecular mechanisms, heterogeneity, and origins. The present study performs whole-brain…
Because of the rapid spread of COVID-19 to almost every part of the globe, huge volumes of data and case studies have been made available, providing researchers with a unique opportunity to find trends and make discoveries like never…
This paper contains an expository account of persistent homology and its usefulness for topological data analysis. An alternative foundation for level-set persistence is presented using sheaves and cosheaves.
Determinants of COVID-19 clinical severity are commonly assessed by transverse or longitudinal studies of the fatality counts. However, the fatality counts depend both on disease clinical severity and transmissibility, as more infected also…
This paper is a cursory study on how topological features are preserved within the internal representations of neural network layers. Using techniques from topological data analysis, namely persistent homology, the topological features of a…
While branching network structures abound in nature, their objective analysis is more difficult than expected because existing quantitative methods often rely on the subjective judgment of branch structures. This problem is particularly…
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…
We present a machine learning approach that leverages persistent homology to classify bacterial flagellar motors into two functional states: rotated and stalled. By embedding protein structural data into a topological framework, we extract…
Understanding the structure of the brain, and how it changes with time and disease, is a core goal of structural neuroimaging. Contemporary approaches to structural brain analysis are dominated by voxel-wise, mass-univariate methods such as…
The objective of this study is to develop a robust deep learning-based framework to distinguish COVID-19, Community-Acquired Pneumonia (CAP), and Normal cases based on chest CT scans acquired in different imaging centers using various…
Topological data analysis (TDA) uncovers crucial properties of objects in medical imaging. Methods based on persistent homology have demonstrated their advantages in capturing topological features that traditional deep learning methods…
Recently, the outbreak of Coronavirus Disease 2019 (COVID-19) has spread rapidly across the world. Due to the large number of affected patients and heavy labor for doctors, computer-aided diagnosis with machine learning algorithm is…
We propose a method, based on persistent homology, to uncover topological properties of a priori unknown covariates of neuron activity. Our input data consist of spike train measurements of a set of neurons of interest, a candidate list of…
In a worldwide health crisis as exigent as COVID-19, there has become a pressing need for rapid, reliable diagnostics. Currently, popular testing methods such as reverse transcription polymerase chain reaction (RT-PCR) can have high false…