The fundamental model of all solid crystalline materials is a periodic set of atomic centers considered up to rigid motion in Euclidean space. The major obstacle to materials discovery was highly ambiguous representations of periodic crystals that didn't allow fast and reliable comparisons and led to numerous (near-) duplicates in many databases of experimental and simulated crystals. This paper exemplarily resolves the ambiguity by invariants, which are descriptors without false negatives.The new Pointwise Distance Distributions (PDD) is a numerical matrix with a near-linear time complexity and an exactly computable metric. The strongest theoretical result is generic completeness (absence of false positives) for all finite and periodic sets of points in any dimension. The strength of PDD is shown by 200B+ pairwise comparisons of all periodic structures in the world's largest collection (Cambridge Structural Database) of existing materials over two days on a modest desktop.

The fundamental model of all solid crystalline materials is a periodic set of atomic centers considered up to rigid motion in Euclidean space. The major obstacle to materials discovery was highly ambiguous representations of periodic crystals that didn't allow fast and reliable comparisons and led to numerous (near-) duplicates in many databases of experimental and simulated crystals. This paper exemplarily resolves the ambiguity by invariants, which are descriptors without false negatives.The new Pointwise Distance Distributions (PDD) is a numerical matrix with a near-linear time complexity and an exactly computable metric. The strongest theoretical result is generic completeness (absence of false positives) for all finite and periodic sets of points in any dimension. The strength of PDD is shown by 200B pairwise comparisons of all periodic structures in the world's largest collection (Cambridge Structural Database) of existing materials over two days on a modest desktop.

The effectiveness of machine learning algorithms depends on the qua lity and amount of data and the operationalization and interpretation by the human analyst . In humanitarian response, data is often lacking or overburdening, thus ambiguous, and t he time - scarce, volatile, insecure environments of humanitarian activities are likely to inflict cognitive biases. This paper proposes to research the effects of data ambiguity and cognitive biases on the interpretability of machine learning algorithms in humanitarian decision making .