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The need for comparison methods between crystal structures led the research to look for proper descriptors that could encode the chemical properties of different materials. Many crystal structures exist in theory, but only some of them may be synthesized in a laboratory and used in the real world for practical applications. To discover new materials, Crystal Structure Prediction is vital in predicting various crystal structure forms or generating new ones by building blocks or molecules. Usually, a structure prediction computes chemical features that are not correct properties because they do not consider the entire 3-dimensional structure of a crystal. However, they rely on rules considering only the type of particles involved. For example, some chemical properties are used frequently to select a good candidate for synthesis because, in theory, they could tell if a crystal may exist in its solid form under some environmental conditions. This thesis project aims to design and develop new geometric tools or properties that can properly distinguish 3-dimensional structures starting from the raw atom coordinates. The Geometric features developed in this document are fast properties or numerical characteristics that map crystal structure to a different space for a more reliable and efficient comparison. Firstly, we solved the comparison problem between crystal lattices by designing a property that maps a crystal lattice to the space of polyhedra and a metric that can distinguish them. Secondly, we designed a new and faster geometric property that relies on vectors of interatomic distances that are proved to change continuously under atom perturbations. Finally, the chemical property prediction was addressed in our last work, where we attempted to predict the chemical properties of crystals by using our geometric features.

Crystal Structure Prediction (CSP) aims to discover solid crystalline materials by optimizing periodic arrangements of atoms, ions or molecules. CSP takes weeks of supercomputer time because of slow energy minimizations for millions of simulated crystals. The lattice energy is a key physical property, which determines thermodynamic stability of a crystal but has no simple analytic expression. Past machine learning approaches to predict the lattice energy used slow crystal descriptors depending on manually chosen parameters. The new area of Periodic Geometry offers much faster isometry invariants that are also continuous under perturbations of atoms. Our experiments on simulated crystals confirm that a small distance between the new invariants guarantees a small difference of energies. We compare several kernel methods for invariant-based predictions of energy and achieve the mean absolute error of less than 5kJ/mole or 0.05eV/atom on a dataset of 5679 crystals., Comment: To appear in the proceedings of DACOMSIN (Data and Computation for Materials Science and Innovation) 2021, https://en.misis.ru/university/colleges/sound/thermochemistry/dacomsin/

This paper develops a new continuous approach to a similarity between periodic lattices of ideal crystals. Quantifying a similarity between crystal structures is needed to substantially speed up the Crystal Structure Prediction, because the prediction of many target properties of crystal structures is computationally slow and is essentially repeated for many nearly identical simulated structures. The proposed distances between arbitrary periodic lattices of crystal structures are invariant under all rigid motions, satisfy the metric axioms and continuity under atomic perturbations. The above properties make these distances ideal tools for clustering and visualizing large datasets of crystal structures. All the conclusions are rigorously proved and justified by experiments on real and simulated crystal structures reported in the Nature 2017 paper "Functional materials discovery using energy-structure-function maps"., Comment: Paper accepted in Crystal Research and Technology Journal

Background: It has been reported that individuals with chronic ankle instability (CAI) show motor control abnormalities. The study of muscle activations by means of surface electromyography (sEMG) plays a key role in understanding some of the features of movement abnormalities. Research question: Do common sEMG activation abnormalities and strategies exists across different functional movements? Methods: Literature review was conducted on PubMed, Web-of-Science and Cochrane databases. Studies published between 2000 and 2020 that assessed muscle activations by means of sEMG during any type of functional task in individuals with CAI, and used healthy individuals as controls, were included. Methodological quality was assessed using the modified Downs&Black checklist. Since the methodologies of different studies were heterogeneous, no meta-analysis was conducted. Results: A total of 63 articles investigating muscle activations during gait, running, responses to perturbations, landing and hopping, cutting and turning; single-limb stance, star excursion balance task, forward lunges, ball-kicking, y-balance test and single-limb squatting were considered. Individuals with CAI showed a delayed activation of the peroneus longus in response to sudden inversion perturbations, in transitions between double- and single-limb stance, and in landing on unstable surfaces. Apparently, while walking on ground there are no differences between CAI and controls, walking on a treadmill increases the variability of muscles activations, probably as a "safety strategy" to avoid ankle inversion. An abnormal activation of the tibialis anterior was observed during a number of tasks. Finally, hip/spine muscles were activated before ankle muscles in CAI compared to controls. Conclusion: Though the methodology of the studies herein considered is heterogeneous, this review shows that the peroneal and tibialis anterior muscles have an abnormal activation in CAI individuals. These individuals also show a proximal muscle activation strategy during the performance of balance challenging tasks. Future studies should investigate whole-body muscle activation abnormalities in CAI individuals.