Miroslav Kramár

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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)
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)
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)
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)
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