Mathematics Commons^™

The Dope Distance Is Sic: A Stable, Informative, And Computable Metric On Ordered Merge Trees, Jose Arbelo, Antonio Delgado, Charley Kirk, Zach Schlamowitz

Mathematics Summer Fellows

When analyzing time series data, it is often of interest to categorize them based on how different they are. We define a new dissimilarity measure between time series: Dynamic Ordered Persistence Editing (DOPE). DOPE satisfies metric properties, is stable to noise, is as informative as alternative approaches, and efficiently computable. Satisfying these properties simultaneously makes DOPE of interest to both theoreticians and data scientists alike.

The Cohomology Of The Mod 2 Steenrod Algebra, Robert R. Bruner, John Rognes

Open Data at Wayne State

The dataset contains a minimal resolution of the mod 2 Steenrod algebra in the range 0 <= s <= 128, 0 <= t <= 200, together with chain maps for each cocycle in that range and for the squaring operation Sq^0 in the cohomology of the Steenrod algebra. The included document CohomA2.pdf explains the contents and usage of the dataset in detail (also available as supplemental material in this record).

Dataset is also available at the NIRD Research Data Archive, https://doi.org/10.11582/2021.00077; Data Description also available at arXiv.org, https://doi.org/10.48550/arXiv.2109.13117.

Software For A Conformally Invariant Yang-Mills Type Energy And Equation On 6-Manifolds, Lawrence Peterson

Datasets

The author has developed some new computer software and has used it, together with Mathematica and John M. Lee's Ricci software package, to verify many of the results in the article "A Conformally Invariant Yang-Mills Type Energy and Equation on 6-Manifolds" (arXiv:2107.08515). The author's new software is posted here, along with the Ricci package and a special guidelines file. One should read this guidelines file before studying or using the software.

A New Non-Inheriting Homogeneous Solution Of The Einstein-Maxwell Equations With Cosmological Term, Charles G. Torre

Research Vignettes

No abstract provided.

When Is A Linear Connection A Metric Connection?, Ian M. Anderson, Charles G. Torre

Tutorials on... in 1 hour or less

In this worksheet we use the DG software to answer the following question: When is there a metric tensor on M whose Christoffel symbols coincide with the components of a given linear connection?

The Differentialgeometry Package, Ian M. Anderson, Charles G. Torre

Downloads

This is the entire DifferentialGeometry package, a zip file (DifferentialGeometry.zip) containing (1) a Maple Library file, DifferentialGeometryUSU.mla, (2) a Maple help file DifferentialGeometry.help, (3) a Maple Library file, DGApplicatons.mla. This is the latest version of the DifferentialGeometry software; it supersedes what is released with Maple.

Installation instructions

What's New In Differentialgeometry Release Dg2022, Ian M. Anderson, Charles G. Torre

Tutorials on... in 1 hour or less

This Maple worksheet demonstrates the salient new features and functionalities of the 2022 release of the DifferentialGeometry software package.

The De Rham Decomposition Theorem, Ian M. Anderson, Charles G. Torre

Tutorials on... in 1 hour or less

In this worksheet we show how the DG software provides for a local implementation of the de Rham decomposition theorem for Riemannian manifolds.