1,302 research outputs found
A Randomized Incremental Algorithm for the Hausdorff Voronoi Diagram of Non-crossing Clusters
In the Hausdorff Voronoi diagram of a family of \emph{clusters of points} in
the plane, the distance between a point and a cluster is measured as
the maximum distance between and any point in , and the diagram is
defined in a nearest-neighbor sense for the input clusters. In this paper we
consider %El."non-crossing" \emph{non-crossing} clusters in the plane, for
which the combinatorial complexity of the Hausdorff Voronoi diagram is linear
in the total number of points, , on the convex hulls of all clusters. We
present a randomized incremental construction, based on point location, that
computes this diagram in expected time and expected
space. Our techniques efficiently handle non-standard characteristics of
generalized Voronoi diagrams, such as sites of non-constant complexity, sites
that are not enclosed in their Voronoi regions, and empty Voronoi regions. The
diagram finds direct applications in VLSI computer-aided design.Comment: arXiv admin note: substantial text overlap with arXiv:1306.583
Exploring the high-pressure materials genome
A thorough in situ characterization of materials at extreme conditions is
challenging, and computational tools such as crystal structural search methods
in combination with ab initio calculations are widely used to guide experiments
by predicting the composition, structure, and properties of high-pressure
compounds. However, such techniques are usually computationally expensive and
not suitable for large-scale combinatorial exploration. On the other hand,
data-driven computational approaches using large materials databases are useful
for the analysis of energetics and stability of hundreds of thousands of
compounds, but their utility for materials discovery is largely limited to
idealized conditions of zero temperature and pressure. Here, we present a novel
framework combining the two computational approaches, using a simple linear
approximation to the enthalpy of a compound in conjunction with
ambient-conditions data currently available in high-throughput databases of
calculated materials properties. We demonstrate its utility by explaining the
occurrence of phases in nature that are not ground states at ambient conditions
and estimating the pressures at which such ambient-metastable phases become
thermodynamically accessible, as well as guiding the exploration of
ambient-immiscible binary systems via sophisticated structural search methods
to discover new stable high-pressure phases.Comment: 14 pages, 6 figure
Copula models for epidemiological research and practice
Investigating associations between random variables (rvs) is one of many topics in the heart of statistical science. Graphical displays show emerging patterns between rvs, and the strength of their association is conventionally quantified via correlation coefficients. When two or more of these rvs are thought of as outcomes, their association is governed by a joint probability distribution function (pdf). When the joint pdf is bivariate normal, scalar correlation coefficients will produce a satisfactory summary of the association, otherwise alternative measures are needed. Local dependence functions, together with their corresponding graphical displays, quantify and show how the strength of the association varies across the span of the data. Additionally, the multivariate distribution function can be explicitly formulated and explored. Copulas model joint distributions of varying shapes by combining the separate (univariate) marginal cumulative distribution functions of each rv under a specified correlation structure. Copula models can be used to analyse complex relationships and incorporate covariates into their parameters. Therefore, they offer increased flexibility in modelling dependence between rvs. Copula models may also be used to construct bivariate analogues of centiles, an application for which few references are available in the literature though it is of particular interest for many paediatric applications. Population centiles are widely used to highlight children or adults who have unusual univariate outcomes. Whilst the methodology for the construction of univariate centiles is well established there has been very little work in the area of bivariate analogues of centiles where two outcomes are jointly considered. Conditional models can increase the efficiency of centile analogues in detection of individuals who require some form of intervention. Such adjustments can be readily incorporated into the modelling of the marginal distributions and of the dependence parameter within the copula model
Navigating phase diagram complexity to guide robotic inorganic materials synthesis
Efficient synthesis recipes are needed both to streamline the manufacturing
of complex materials and to accelerate the realization of theoretically
predicted materials. Oftentimes the solid-state synthesis of multicomponent
oxides is impeded by undesired byproduct phases, which can kinetically trap
reactions in an incomplete non-equilibrium state. We present a thermodynamic
strategy to navigate high-dimensional phase diagrams in search of precursors
that circumvent low-energy competing byproducts, while maximizing the reaction
energy to drive fast phase transformation kinetics. Using a robotic inorganic
materials synthesis laboratory, we perform a large-scale experimental
validation of our precursor selection principles. For a set of 35 target
quaternary oxides with chemistries representative of intercalation battery
cathodes and solid-state electrolytes, we perform 224 reactions spanning 27
elements with 28 unique precursors. Our predicted precursors frequently yield
target materials with higher phase purity than when starting from traditional
precursors. Robotic laboratories offer an exciting new platform for data-driven
experimental science, from which we can develop new insights into materials
synthesis for both robot and human chemists
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