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We exploit recent advances in computational topology to study the compressibility of various proteins found in the Protein Data Bank (PDB). Our fundamental tool is the persistence diagram, a topological invariant which captures the sizes and robustness of geometric features such as tunnels and cavities in protein molecules. Based on certain physical and… (More)

- Dane Taylor, Florian Klimm, +4 authors Peter J. Mucha
- Nature communications
- 2015

Social and biological contagions are influenced by the spatial embeddedness of networks. Historically, many epidemics spread as a wave across part of the Earth's surface; however, in modern contagions long-range edges-for example, due to airline transportation or communication media-allow clusters of a contagion to appear in distant locations. Here we study… (More)

In this paper we partially clarify the relation between the compressibility of a protein and its molecular geometric structure. To identify and understand the relevant topological features within a given protein, we model its molecule as an alpha filtration and hence obtain multi-scale insight into the structure of its tunnels M. Gameiro Instituto de… (More)

- Miroslav Kramár, Rachel Levanger, +5 authors Konstantin Mischaikow
- 2015

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 flow field patterns from numerical simulations of two important problems in fluid dynamics: Kolmogorov flow and Rayleigh-Bénard convection. For each image we compute a persistence… (More)

- Jan Bouwe van den Berg, Miroslav Kramár, Robert C. Vandervorst
- SIAM J. Applied Dynamical Systems
- 2011

In second order Lagrangian systems bifurcation branches of periodic solutions preserve certain topological invariants. These invariants are based on the observation that periodic orbits of a second order Lagrangian lie on 3-dimensional (non-compact) energy manifolds and the periodic orbits may have various linking and knotting properties. The main… (More)

- Jonathan Jaquette, Miroslav Kramár
- Math. Comput.
- 2017

Biological and physical systems often exhibit distinct structures at different spatial/temporal scales. Persistent homology is an algebraic tool that provides a mathematical framework for analyzing the multi-scale structures frequently observed in nature. In this paper a theoretical framework for the algorithmic computation of an arbitrarily good… (More)

- H N NEU, M S KRAMAR, W ANTHONY
- Archives of physical medicine and rehabilitation
- 1957

- M Kramar
- Psihoterapija
- 1973

- Dane Taylor, Florian Klimm, +4 authors Peter J. Mucha
- ArXiv
- 2014

- Dane Taylor, Florian Klimm, +4 authors Peter J. Mucha
- Nature communications
- 2015

In the sixth paragraph of the Methods section of this article, there is a typographical error in the equation [1 À q(t)/N]d NG. The correct version of the equation reads as follows: ½1 À qðtÞ=N d ðNGÞ

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