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High-energy electrons induce sample damage and motion at the nanoscale to fundamentally limit the determination of molecular structures by electron diffraction. Using a fast event-based electron counting (EBEC) detector, we characterize beam-induced, dynamic, molecular crystal lattice reorientations (BIRs). These changes are sufficiently large to bring reciprocal lattice points entirely in or out of intersection with the sphere of reflection, occur as early events in the decay of diffracted signal due to radiolytic damage, and coincide with beam-induced migrations of crystal bend contours within the same fluence regime and at the same illuminated location on a crystal. These effects are observed in crystals of biotin, a series of amino acid metal chelates, and a six-residue peptide, suggesting that incident electrons inevitably warp molecular lattices. The precise orientation changes experienced by a given microcrystal are unpredictable but are measurable by indexing individual diffraction patterns during beam-induced decay. Reorientations can often tilt a crystal lattice several degrees away from its initial position before irradiation, and for an especially beam-sensitive Zn(II)-methionine chelate, are associated with dramatic crystal quakes prior to 1 e⁻ Å⁻²electron beam fluence accumulates. Since BIR coincides with the early stages of beam-induced damage, it echoes the beam-induced motion observed in single-particle cryoEM. As with motion correction for cryoEM imaging experiments, accounting for BIR-induced errors during data processing could improve the accuracy of MicroED data. 

Abstract Maximum likelihood estimation is among the most widely-used methods for inferring phylogenetic trees from sequence data. This paper solves the problem of computing solutions to the maximum likelihood problem for 3-leaf trees under the 2-state symmetric mutation model (CFN model). Our main result is a closed-form solution to the maximum likelihood problem for unrooted 3-leaf trees, given generic data; this result characterizes all of the ways that a maximum likelihood estimate can fail to exist for generic data and provides theoretical validation for predictions made in Parks and Goldman (Syst Biol 63(5):798–811, 2014). Our proof makes use of both classical tools for studying group-based phylogenetic models such as Hadamard conjugation and reparameterization in terms of Fourier coordinates, as well as more recent results concerning the semi-algebraic constraints of the CFN model. To be able to put these into practice, we also give a complete characterization to test genericity.