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- Miroslav Kramár, Rachel Levanger, +5 authors Konstantin Mischaikow
- 2016

We use persistent homology to build a quantitative understanding of large complex systems that are driven far-fromequilibrium; in particular, we analyze image time series of ow eld patterns from… (More)

- Shaun Harker, Miroslav Kramár, Rachel Levanger, Konstantin Mischaikow
- J. Appl. Comput. Topol.
- 2018

We present a generalization of the induced matching theorem of as reported by Bauer and Lesnick (in: Proceedings of the thirtieth annual symposium computational geometry 2014) and use it to prove a… (More)

- Robert Ghrist, Rachel Levanger, Huy Mai
- J. Appl. Comput. Topol.
- 2018

The Euler calculus—an integral calculus based on Euler characteristic as a valuation on constructible functions—is shown to be an incisive tool for answering questions about injectivity and… (More)

For positive semidefinite $n\times n$ matrices $A$ and $B$, the singular value inequality $(2+t)s_{j}(A^{r}B^{2-r}+A^{2-r}B^{r})\leq 2s_{j}(A^{2}+tAB+B^{2})$ is shown to hold for $r=\frac{1}{2}, 1,… (More)

We explore the chaotic dynamics of Rayleigh-B\'enard convection using large-scale, parallel numerical simulations for experimentally accessible conditions. We quantify the connections between the… (More)

We present a generalization of the induced matching theorem of [1] and use it to prove a generalization of the algebraic stability theorem for R-indexed pointwise finitedimensional persistence… (More)

- Jeffrey Tithof, Balachandra Suri, +6 authors Michael Francis Schatz
- 2014

- Brett Tregoning, Rachel Levanger, +4 authors Michael Francis Schatz
- 2018

- Jeffrey Tithof, Balachandra Suri, +5 authors Michael Francis Schatz
- 2015

We probe the effectiveness of using topological defects to characterize the leading Lyapunov vector for a high-dimensional chaotic convective flow field. This is accomplished using large-scale… (More)