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While topological materials are not restricted to crystals, there is no efficient method to diagnose topology in non-crystalline solids such as amorphous materials. Here we introduce the structural spillage, a new indicator that predicts…
In many applications, data cluster. Failing to take the cluster structure into consideration generally leads to underestimated variances of point estimators and inflated type I errors in hypothesis tests. Many circumstance-dependent…
Conformal prediction, a post-hoc, distribution-free, finite-sample method of uncertainty quantification that offers formal coverage guarantees under the assumption of data exchangeability. Unfortunately, the resulting uncertainty regions…
In steels and single-crystal superalloys the control of the formation of topologically close-packed (TCP) phases is critical for the performance of the material. The structural stability of TCP phases in multi-component transition-metal…
The crystalline period map is a tool for linearizing $p$-divisible groups. It has been applied to study the Langlands correspondences, and has possible applications to the homotopy groups of spheres. The original construction of the period…
Among metallic alloys, ceramics, and even common compounds such as water ice, it is usual to find materials in which crystalline order is expressed as a probability. In such cases, one or more sites within a crystal can be occupied by…
The prediction of material structure from chemical composition has been a long-standing challenge in natural science. Although there have been various methodological developments and successes with computer simulations, the prediction of…
Nuclear Magnetic Resonance (NMR) spectroscopy is particularly well-suited to determine the structure of molecules and materials in powdered form. Structure determination usually proceeds by finding the best match between experimentally…
Understanding the multiplicity of stellar systems and the correlations between their hierarchical components provides crucial insights into star formation processes. If binary companions form independently in each component of a wide binary…
In recent years, there has been a growing demand to discern clusters of subjects in datasets characterized by a large set of features. Often, these clusters may be highly variable in size and present partial hierarchical structures. In this…
Mixtures of bare atomic nuclei on a nearly uniform degenerate electron background are a realistic model of matter in the interior of white dwarfs. Despite tremendous progress in understanding their phase diagrams achieved mainly via…
We present a simple and general method for construction of localized orbitals to describe electronic structure of extended periodic metals and insulators as well as confined systems. Spatial decay of these orbitals is found to exhibit…
Structures and properties of many inorganic compounds have been collected historically. However, it only covers a very small portion of possible inorganic crystals, which implies the presence of numerous currently unknown compounds. A…
Predicting the ground state of alloy systems is challenging due to the large number of possible configurations. We identify an easily computed descriptor for the stability of binary surface alloys, the effective coordination number…
In materials discovery, the integration of first-principles calculations with machine learning techniques has been actively studied for two key tasks: crystal structure prediction, which searches for stable structures given a chemical…
Rajasekharan and Girgis reported that binary systems with intermetallic compounds of a particular crystal structure form a straight line on a map using Miedema parameters. In this paper, the universality of that observation is examined.…
A hierarchical scheme for clustering data is presented which applies to spaces with a high number of dimension ($N_{_{D}}>3$). The data set is first reduced to a smaller set of partitions (multi-dimensional bins). Multiple clustering…
Clustering aims to group unlabelled samples based on their similarities. It has become a significant tool for the analysis of high-dimensional data. However, most of the clustering methods merely generate pseudo labels and thus are unable…
Generative models for materials, especially inorganic crystals, hold potential to transform the theoretical prediction of novel compounds and structures. Advancement in this field depends on robust benchmarks and minimal, information-rich…