RESUMO
Encoding the complex features of an energy landscape is a challenging task, and often, chemists pursue the most salient features (minima and barriers) along a highly reduced space, i.e., two- or three-dimensions. Even though disconnectivity graphs or merge trees summarize the connectivity of the local minima of an energy landscape via the lowest-barrier pathways, there is much information to be gained by also considering the topology of each connected component at different energy thresholds (or sublevelsets). We propose sublevelset persistent homology as an appropriate tool for this purpose. Our computations on the configuration phase space of n-alkanes from butane to octane allow us to conjecture, and then prove, a complete characterization of the sublevelset persistent homology of the alkane CmH2m+2 Potential Energy Landscapes (PELs), for all m, in all homological dimensions. We further compare both the analytical configurational PELs and sampled data from molecular dynamics simulation using the united and all-atom descriptions of the intramolecular interactions. In turn, this supports the application of distance metrics to quantify sampling fidelity and lays the foundation for future work regarding new metrics that quantify differences between the topological features of high-dimensional energy landscapes.
RESUMO
Sleep patterns vary widely between individuals. We explore methods for identifying populations exhibiting similar sleep patterns in an automated fashion using polysomnography data. Our novel approach applies unsupervised machine learning algorithms to hypnodensities graphs generated by a pre-trained neural network. In a population of 100 subjects we identify two stable clusters whose characteristics we visualize graphically and through estimates of total sleep time. We also find that the hypnodensity representation of the sleep stages produces more robust clustering results than the same methods applied to traditional hypnograms.