DiSCoVeR: a Materials Discovery Screening Tool for High Performance, Unique Chemical Compositions

We present Descending from Stochastic Clustering Variance Regression (DiSCoVeR), a Python tool for identifying high-performing, chemically unique compositions relative to existing compounds using a combination of a chemical distance metric, density-aware dimensionality reduction, and clustering. We introduce several new metrics for materials discovery and validate DiSCoVeR on Materials Project bulk moduli using compound-wise and cluster-wise validation methods. We visualize these via multiobjective Pareto front plots and assign a weighted score to each composition where this score encompasses the trade-off between performance and density-based chemical uniqueness. We explore an additional uniqueness proxy related to property gradients in chemical space. We demonstrate that DiSCoVeR can successfully screen materials for both performance and uniqueness in order to extrapolate to new chemical spaces.

DiSCoVeR: a Materials Discovery Screening Tool for High Performance, Unique Chemical Compositions

We present Descending from Stochastic Clustering Variance Regression (DiSCoVeR), a Python tool for identifying high-performing, chemically unique compositions relative to existing compounds using a combination of a chemical distance metric, density-aware dimensionality reduction, and clustering. We introduce several new metrics for materials discovery and validate DiSCoVeR on Materials Project bulk moduli using compound-wise and cluster-wise validation methods. We visualize these via multiobjective Pareto front plots and assign a weighted score to each composition where this score encompasses the trade-off between performance and density-based chemical uniqueness. We explore an additional uniqueness proxy related to property gradients in chemical space. We demonstrate that DiSCoVeR can successfully screen materials for both performance and uniqueness in order to extrapolate to new chemical spaces.

DiSCoVeR: a Materials Discovery Screening Tool for High Performance, Unique Chemical Compositions

We present Descending from Stochastic Clustering Variance Regression (DiSCoVeR), a Python tool for identifying high-performing, chemically unique compositions relative to existing compounds using a combination of a chemical distance metric, density-aware dimensionality reduction, and clustering. We introduce several new metrics for materials discovery and validate DiSCoVeR on Materials Project bulk moduli using compound-wise and cluster-wise validation methods. We visualize these via multiobjective Pareto front plots and assign a weighted score to each composition where this score encompasses the trade-off between performance and density-based chemical uniqueness. We explore an additional uniqueness proxy related to property gradients in chemical space. We demonstrate that DiSCoVeR can successfully screen materials for both performance and uniqueness in order to extrapolate to new chemical spaces.

Regularity of the time constant for a supercritical Bernoulli percolation

We consider an i.i.d. supercritical bond percolation on Z^d, every edge is open with a probability p > p_c(d), where p_c(d) denotes the critical parameter for this percolation. We know that there exists almost surely a unique infinite open cluster C_p [11]. We are interested in the regularity properties of the chemical distance for supercritical Bernoulli percolation. The chemical distance between two points x, y ∈ C_p corresponds to the length of the shortest path in C_p joining the two points. The chemical distance between 0 and nx grows asymptotically like nµ_p(x). We aim to study the regularity properties of the map p → µ_p in the supercritical regime. This may be seen as a special case of first passage percolation where the distribution of the passage time is G_p = pδ_1 + (1 − p)δ_∞, p > p_c(d). It is already known that the map p → µ_p is continuous (see [10]).

A family of tractable graph metrics

Important data mining problems such as nearest-neighbor search and clustering admit theoretical guarantees when restricted to objects embedded in a metric space. Graphs are ubiquitous, and clustering and classification over graphs arise in diverse areas, including, e.g., image processing and social networks. Unfortunately, popular distance scores used in these applications, that scale over large graphs, are not metrics and thus come with no guarantees. Classic graph distances such as, e.g., the chemical distance and the Chartrand-Kubiki-Shultz distance are arguably natural and intuitive, and are indeed also metrics, but they are intractable: as such, their computation does not scale to large graphs. We define a broad family of graph distances, that includes both the chemical and the Chartrand-Kubiki-Shultz distances, and prove that these are all metrics. Crucially, we show that our family includes metrics that are tractable. Moreover, we extend these distances by incorporating auxiliary node attributes, which is important in practice, while maintaining both the metric property and tractability.