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javaPlex: A Research Software Package for Persistent (Co)Homology
The computation of persistent homology has proven a fundamental component of the nascent field of topological data analysis and computational topology. We describe a new software package forExpand
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Applications of Zigzag Persistence to Topological Data Analysis
The theory of zigzag persistence is a substantial extension of persistent homology, and its development has enabled the investigation of several unexplored avenues in the area of topological dataExpand
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High-resolution, large dynamic range fiber length measurement based on a frequency-shifted asymmetric Sagnac interferometer.
We propose and experimentally demonstrate a single-mode fiber length and dispersion measurement system based on what we believe to be a novel frequency-shifted asymmetric Sagnac interferometerExpand
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Frequency-shifted Mach-Zehnder interferometer for locating multiple weak reflections along a fiber link
We propose and demonstrate a novel technique for measuring fiber lengths and locating multiple weak reflections along the fiber using a low-cost continuous wave source, a folded Mach-ZehnderExpand
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javaPlex: a research platform for persistent homology
The javaPlex software package continues the Stanford tradition of software for persistent homology and cohomology computation. javaPlex in particular is built with explicit aims for ease of use as aExpand
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Homological Coordinatization
In this paper, we review a method for computing and parameterizing the set of homotopy classes of chain maps between two chain complexes. This is then applied to finding topologically meaningful mapsExpand
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Predicting the Date of Authorship of Historical Texts
In this document, we address the following question: Given a piece of text, can we predict its year of authorship? This question is of interest in situations where there is a dispute about the authorExpand
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Properties of Conditional Expectation Operators and Sufficient Subfields
We discuss some properties of conditional expectation operators, and use these facts to prove an interesting counterexample regarding sufficient statistics. In particular, we show that there existsExpand
Topological Classification of Data Sets without an Explicit Metric
A contemporary problem in data analysis is understanding the nature of high dimensional data sets. Given a set of points in a high-dimensional space, a key question is to determine its topologicalExpand
Frequency-shifted interferometer and its applications
We propose a frequency-shifted interferometer and demonstrate its various applications, including fiber length and dispersion measurement, multiple weak reflection sites locating along a fiber link.Expand