Related papers: Determining clinically relevant features in cytome…
Topological data analysis (TDA) detects geometric structure in biological data. However, many TDA algorithms are memory intensive and impractical for massive datasets. Here, we introduce a statistical protocol that reduces TDA's memory…
Epidemic data show the existence of a region of quasi-linear growth (strolling period) of infected cases extending in between waves. We demonstrate that this constitutes evidence for the existence of near time-scale invariance that is…
We apply topological data analysis to the behavior of C. elegans, a widely-studied model organism in biology. In particular, we use topology to produce a quantitative summary of complex behavior which may be applied to high-throughput data.…
This work presents a comparative evaluation of two fundamentally different feature extraction paradigms--Histogram of Oriented Gradients (HOG) and Topological Data Analysis (TDA)--for medical image classification, with a focus on retinal…
Persistent homology is a method for probing topological properties of point clouds and functions. The method involves tracking the birth and death of topological features (2000) as one varies a tuning parameter. Features with short…
Batch effects in high-dimensional Cytometry by Time-of-Flight (CyTOF) data pose a challenge for comparative analysis across different experimental conditions or time points. Traditional batch normalization methods may fail to preserve the…
Real data is often given as a point cloud, i.e. a finite set of points with pairwise distances between them. An important problem is to detect the topological shape of data --- for example, to approximate a point cloud by a low-dimensional…
Topological data analysis (TDA) is an emerging field in mathematics and data science. Its central technique, persistent homology, has had tremendous success in many science and engineering disciplines. However, persistent homology has…
Tools of Topological Data Analysis provide stable summaries encapsulating the shape of the considered data. Persistent homology, the most standard and well studied data summary, suffers a number of limitations; its computations are hard to…
Chromosome conformation capture experiments such as Hi-C are used to map the three-dimensional spatial organization of genomes. One specific feature of the 3D organization is known as topologically associating domains (TADs), which are…
Epidemiologic and genetic studies in chronic obstructive pulmonary disease (COPD) and many complex diseases suggest subgroup disparities (e.g., by sex). We consider this problem from the standpoint of integrative analysis where we combine…
The recent coronavirus disease (COVID-19) outbreak has dramatically increased the public awareness and appreciation of the utility of dynamic models. At the same time, the dissemination of contradictory model predictions has highlighted…
Topological data analysis (TDA) is a rising branch in modern applied mathematics. It extracts topological structures as features of a given space and uses these features to analyze digital data. Persistent homology, one of the central tools…
This paper extends the possibility to examine the underlying curvature of data through the lens of topology by using the Betti curves, tools of Persistent Homology, as key topological descriptors, building on the clique topology approach.…
Segmentation networks are not explicitly imposed to learn global invariants of an image, such as the shape of an object and the geometry between multiple objects, when they are trained with a standard loss function. On the other hand,…
Determining whether two graphs are isomorphic is a fundamental problem with practical applications in areas such as molecular chemistry or social network analysis, yet it remains a challenging task, with exact solutions often being…
Early detection of COVID-19 is vital to control its spread. Deep learning methods have been presented to detect suggestive signs of COVID-19 from chest CT images. However, due to the novelty of the disease, annotated volumetric data are…
In this article, we introduce a Topological Data Analysis (TDA) pipeline for neural spike train data. Understanding how the brain transforms sensory information into perception and behavior requires analyzing coordinated neural population…
Spatial relationships in multi-species data can indicate and affect system outcomes and behaviors, ranging from disease progression in cancer to coral reef resilience in ecology; therefore, quantifying these relationships is an important…
Persistent homology (PH) is a rigorous mathematical theory that provides a robust descriptor of data in the form of persistence diagrams (PDs) which are 2D multisets of points. Their variable size makes them, however, difficult to combine…