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Classifying Crystals of Rounded Tetrahedra and Determining Their Order Parameters Using Dimensionality Reduction.

ABSTRACT: Using simulations we study the phase behavior of a family of hard spherotetrahedra, a shape that interpolates between tetrahedra and spheres. We identify 13 close-packed structures, some with packings that are significantly denser than previously reported. Twelve of these are crystals with unit cells of N = 2 or N = 4 particles, but in the shape regime of slightly rounded tetrahedra we find that the densest structure is a quasicrystal approximant with a unit cell of N = 82 particles. All 13 structures are also stable below close packing, together with an additional 14th plastic crystal phase at the sphere side of the phase diagram, and upon sufficient dilution to packing fractions below 50-60% all structures melt. Interestingly, however, upon compressing the fluid phase, self-assembly takes place spontaneously only at the tetrahedron and the sphere side of the family but not in an intermediate regime of tetrahedra with rounded edges. We describe the local environment of each particle by a set of l-fold bond orientational order parameters q?l, which we use in an extensive principal component analysis. We find that the total packing fraction as well as several particular linear combinations of q?l rather than individual q?l's are optimally distinctive, specifically the differences q?4 - q?6 for separating tetragonal from hexagonal structures and q?4-q?8 for distinguishing tetragonal structures. We argue that these characteristic combinations are also useful as reliable order parameters in nucleation studies, enhanced sampling techniques, or inverse-design methods involving odd-shaped particles in general.

SUBMITTER: van Damme R

PROVIDER: S-EPMC7690044 | biostudies-literature | 2020 Nov

REPOSITORIES: biostudies-literature

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Classifying Crystals of Rounded Tetrahedra and Determining Their Order Parameters Using Dimensionality Reduction.

van Damme Robin R Coli Gabriele M GM van Roij René R Dijkstra Marjolein M

ACS nano 20201026 11

Using simulations we study the phase behavior of a family of hard spherotetrahedra, a shape that interpolates between tetrahedra and spheres. We identify 13 close-packed structures, some with packings that are significantly denser than previously reported. Twelve of these are crystals with unit cells of N = 2 or N = 4 particles, but in the shape regime of slightly rounded tetrahedra we find that the densest structure is a quasicrystal approximant with a unit cell of N = 82 p ...[more]

PMID: 33103878

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Project description:Identifying gene-gene interactions or gene-environment interactions in studies of human complex diseases remains a big challenge in genetic epidemiology. An additional challenge, often forgotten, is to account for important lower-order genetic effects. These may hamper the identification of genuine epistasis. If lower-order genetic effects contribute to the genetic variance of a trait, identified statistical interactions may simply be due to a signal boost of these effects. In this study, we restrict attention to quantitative traits and bi-allelic SNPs as genetic markers. Moreover, our interaction study focuses on 2-way SNP-SNP interactions. Via simulations, we assess the performance of different corrective measures for lower-order genetic effects in Model-Based Multifactor Dimensionality Reduction epistasis detection, using additive and co-dominant coding schemes. Performance is evaluated in terms of power and familywise error rate. Our simulations indicate that empirical power estimates are reduced with correction of lower-order effects, likewise familywise error rates. Easy-to-use automatic SNP selection procedures, SNP selection based on "top" findings, or SNP selection based on p-value criterion for interesting main effects result in reduced power but also almost zero false positive rates. Always accounting for main effects in the SNP-SNP pair under investigation during Model-Based Multifactor Dimensionality Reduction analysis adequately controls false positive epistasis findings. This is particularly true when adopting a co-dominant corrective coding scheme. In conclusion, automatic search procedures to identify lower-order effects to correct for during epistasis screening should be avoided. The same is true for procedures that adjust for lower-order effects prior to Model-Based Multifactor Dimensionality Reduction and involve using residuals as the new trait. We advocate using "on-the-fly" lower-order effects adjusting when screening for SNP-SNP interactions using Model-Based Multifactor Dimensionality Reduction analysis.

Dataset Information

Classifying Crystals of Rounded Tetrahedra and Determining Their Order Parameters Using Dimensionality Reduction.

Publications

Classifying Crystals of Rounded Tetrahedra and Determining Their Order Parameters Using Dimensionality Reduction.

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