Spin-orbit interaction affects the band structure of topological insulators beyond the opening of an inverted gap in the bulk bands, and the understanding of its effects on the surface states is of primary importance to access the underlying physics of these exotic states. Here, we propose an $\textit{ab initio}$ approach benchmarked by pump-probe angle-resolved photoelectron spectroscopy data to model the effect of spin-orbit coupling on the surface states of a topological insulator. The critical novelty of our approach lies in the possibility of accounting for a partial transfer of the spin-orbit coupling to the surface states, mediated by the hybridization with the surface resonance states. In topological insulators, the fraction of transferred spin-orbit coupling influences the strength of the hexagonal warping of the surface states, which we use as a telltale of the capability of our model to reproduce the experimental dispersion. The comparison between calculations and measurements, of both the unoccupied and part of the occupied Dirac cone, indicates that the fraction of spin-orbit coupling transferred to the surface states by hybridization with the resonance states is between 70% and 85% of its full atomic value. This offers a valuable insight to improve the modeling of surface state properties in topological insulators for both scientific purposes and technological applications.

Cryo-electron microscopy (cryo-EM) studies using single particle reconstruction are extensively used to reveal structural information on macromolecular complexes. Aiming at the highest achievable resolution, state of the art electron microscopes automatically acquire thousands of high-quality micrographs. Particles are detected on and boxed out from each micrograph using fully- or semi-automated approaches. However, the obtained particles still require laborious manual post-picking classification, which is one major bottleneck for single particle analysis of large datasets. We introduce MAPPOS, a supervised post-picking strategy for the classification of boxed particle images, as additional strategy adding to the already efficient automated particle picking routines. MAPPOS employs machine learning techniques to train a robust classifier from a small number of characteristic image features. In order to accurately quantify the performance of MAPPOS we used simulated particle and non-particle images. In addition, we verified our method by applying it to an experimental cryo-EM dataset and comparing the results to the manual classification of the same dataset. Comparisons between MAPPOS and manual post-picking classification by several human experts demonstrated that merely a few hundred sample images are sufficient for MAPPOS to classify an entire dataset with a human-like performance. MAPPOS was shown to greatly accelerate the throughput of large datasets by reducing the manual workload by orders of magnitude while maintaining a reliable identification of non-particle images.