Robin Belton
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Discrete Level Set Persistence for Finite Discrete Functions Open
We study sublevel set and superlevel set persistent homology on discrete functions through the perspective of finite ordered sets of both linearly ordered and cyclically ordered domains. Finite ordered sets also serve as the codomain of ou…
Any Graph is a Mapper Graph Open
The Mapper algorithm is a popular tool for visualization and data exploration in topological data analysis. We investigate an inverse problem for the Mapper algorithm: Given a dataset $X$ and a graph $G$, does there exist a set of Mapper p…
G-Mapper: Learning a Cover in the Mapper Construction Open
The Mapper algorithm is a visualization technique in topological data analysis (TDA) that outputs a graph reflecting the structure of a given dataset. However, the Mapper algorithm requires tuning several parameters in order to generate a …
View article: Extremal event graphs: A (stable) tool for analyzing noisy time series data
Extremal event graphs: A (stable) tool for analyzing noisy time series data Open
This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Foundations of Data Science following peer review. The definitive publisher-authenticated version [Extremal event graphs: A (stable) tool for analyzi…
View article: Extremal Event Graphs: A (Stable) Tool for Analyzing Noisy Time Series Data
Extremal Event Graphs: A (Stable) Tool for Analyzing Noisy Time Series Data Open
Local maxima and minima, or extremal events, in experimental time series can be used as a coarse summary to characterize data. However, the discrete sampling in recording experimental measurements suggests uncertainty on the true timing of…
Combinatorial Conditions for Directed Collapsing Open
The purpose of this article is to study directed collapsibility of directed Euclidean cubical complexes. One application of this is in the nontrivial task of verifying the execution of concurrent programs. The classical definition of colla…
An obstruction to contractibility of spaces of directed paths. Open
Defining homotopy or collapsibility in directed topological spaces is surprisingly difficult. In the directed setting, the spaces of directed paths between fixed initial and terminal points are the defining feature for distinguishing diffe…
Towards Directed Collapsibility Open
In the directed setting, the spaces of directed paths between fixed initial and terminal points are the defining feature for distinguishing different directed spaces. The simplest case is when the space of directed paths is homotopy equiva…
Loss of TXNIP enhances peritoneal metastasis and can be abrogated by dual TORC1/2 inhibition Open
Peritoneal metastasis (PM) is a debilitating consequence of multiple cancers. As cancer cells lose tonic signaling related to attachment dependence, critical morphologic shifts result in alteration of the transcriptome. Identifying key gen…
Learning Simplicial Complexes from Persistence Diagrams Open
Topological Data Analysis (TDA) studies the shape of data. A common topological descriptor is the persistence diagram, which encodes topological features in a topological space at different scales. Turner, Mukeherjee, and Boyer showed that…
A shape-context model for matching placental chorionic surface vascular networks Open
Placental chorionic surface vascular networks (PCSVNs) are essential high-capacitance, low-resistance distribution and drainage networks, and are hence important to placental function and to fetal and newborn health. It was hypothesized th…