Heterogeneity in susceptibility dictates the order of epidemiological models

The fundamental models of epidemiology describe the progression of an infectious disease through a population using compartmentalized differential equations, but do not incorporate population-level heterogeneity in infection susceptibility. We show that variation strongly influences the rate of infection, while the infection process simultaneously sculpts the susceptibility distribution. These joint dynamics influence the force of infection and are, in turn, influenced by the shape of the initial variability. Intriguingly, we find that certain susceptibility distributions (the exponential and the gamma) are unchanged through the course of the outbreak, and lead naturally to power-law behavior in the force of infection; other distributions often tend towards these "eigen-distributions" through the process of contagion. The power-law behavior fundamentally alters predictions of the long-term infection rate, and suggests that first-order epidemic models that are parameterized in the exponential-like phase may systematically and significantly over-estimate the final severity of the outbreak

The phase stability of large-size nanoparticle alloy catalysts at ab initio quality using a nearsighted force-training approach

CoPt nanoparticle catalysts are integral to commercial fuel cells. Such systems are prohibitive to fully characterize with electronic structure calculations. Machine-learned potentials offer a scalable solution; however, such potentials are only reliable if representative training data can be employed, which typically requires large electronic structure calculations. Here, we use the nearsighted-force training approach to make high-fidelity machine-learned predictions on large nanoparticles with $>$5,000 atoms using only systematically generated small structures ranging from 38-168 atoms. The resulting ensemble model shows good accuracy and transferability in describing relative energetics for CoPt nanoparticles with various shapes, sizes and Co compositions. It is found that the fcc(100) surface is more likely to form a L1$_0$ ordered structure than the fcc(111) surface. The energy convex hull of the icosahedron shows the most stable particles have Pt-rich skins and Co-rich underlayers. Although the truncated octahedron is the most stable shape across all sizes of Pt nanoparticles, a crossover to icosahedron exists due to a large downshift of surface energy for CoPt nanoparticle alloys. The downshift can be attributed to strain release on the icosahedron surface due to Co alloying. We introduced a simple empirical model to describe the role of Co alloying in the crossover for CoPt nanoparticles. With Monte-Carlo simulations we additionally searched for the most stable atomic arrangement for a truncated octahedron with equal Pt and Co compositions, and also we studied its order-disorder phase transition. We validated the most stable configurations with a new highly scalable density functional theory code called SPARC. Lastly, the order-disorder phase transition for a CoPt nanoparticle exhibits a lower transition temperature and a smoother transition, compared to the bulk CoPt alloy.Comment: 26 pages, 8 figure

Ab-initio investigation of finite size effects in rutile titania nanoparticles with semilocal and nonlocal density functionals

In this work, we employ hybrid and generalized gradient approximation (GGA) level density functional theory (DFT) calculations to investigate the convergence of surface properties and band structure of rutile titania (TiO$_2$) nanoparticles with particle size. The surface energies and band structures are calculated for cuboidal particles with minimum dimension ranging from 3.7 \r{A} (24 atoms) to 10.3 \r{A} (384 atoms) using a highly-parallel real-space DFT code to enable hybrid level DFT calculations of larger nanoparticles than are typically practical. We deconvolute the geometric and electronic finite size effects in surface energy, and evaluate the influence of defects on band structure and density of states (DOS). The electronic finite size effects in surface energy vanish when the minimum length scale of the nanoparticles becomes greater than 10 \r{A}. We show that this length scale is consistent with a computationally efficient numerical analysis of the characteristic length scale of electronic interactions. The surface energy of nanoparticles having minimum dimension beyond this characteristic length can be approximated using slab calculations that account for the geometric defects. In contrast, the finite size effects on the band structure is highly dependent on the shape and size of these particles. The DOS for cuboidal particles and more realistic particles constructed using the Wulff algorithm reveal that defect states within the bandgap play a key role in determining the band structure of nanoparticles and the bandgap does not converge to the bulk limit for the particle sizes investigated

ElectroLens: Understanding Atomistic Simulations Through Spatially-resolved Visualization of High-dimensional Features

In recent years, machine learning (ML) has gained significant popularity in the field of chemical informatics and electronic structure theory. These techniques often require researchers to engineer abstract "features" that encode chemical concepts into a mathematical form compatible with the input to machine-learning models. However, there is no existing tool to connect these abstract features back to the actual chemical system, making it difficult to diagnose failures and to build intuition about the meaning of the features. We present ElectroLens, a new visualization tool for high-dimensional spatially-resolved features to tackle this problem. The tool visualizes high-dimensional data sets for atomistic and electron environment features by a series of linked 3D views and 2D plots. The tool is able to connect different derived features and their corresponding regions in 3D via interactive selection. It is built to be scalable, and integrate with existing infrastructure.Comment: accepted to IEEE visualization 2019 conferenc

Soft and transferable pseudopotentials from multi-objective optimization

Ab initio pseudopotentials are a linchpin of modern molecular and condensed matter electronic structure calculations. In this work, we employ multi-objective optimization to maximize pseudopotential softness while maintaining high accuracy and transferability. To accomplish this, we develop a formulation in which softness and accuracy are simultaneously maximized, with accuracy determined by the ability to reproduce all-electron energy differences between Bravais lattice structures, whereupon the resulting Pareto frontier is scanned for the softest pseudopotential that provides the desired accuracy in established transferability tests. We employ an evolutionary algorithm to solve the multi-objective optimization problem and apply it to generate a comprehensive table of optimized norm-conserving Vanderbilt (ONCV) pseudopotentials (https://github.com/SPARC-X/SPMS-psps). We show that the resulting table is softer than existing tables of comparable accuracy, while more accurate than tables of comparable softness. The potentials thus afford the possibility to speed up calculations in a broad range of applications areas while maintaining high accuracy.Comment: 13 pages, 4 figure

Kohn-Sham accuracy from orbital-free density functional theory via Δ\Delta-machine learning

We present a $\Delta$-machine learning model for obtaining Kohn-Sham accuracy from orbital-free density functional theory (DFT) calculations. In particular, we employ a machine learned force field (MLFF) scheme based on the kernel method to capture the difference between Kohn-Sham and orbital-free DFT energies/forces. We implement this model in the context of on-the-fly molecular dynamics simulations, and study its accuracy, performance, and sensitivity to parameters for representative systems. We find that the formalism not only improves the accuracy of Thomas-Fermi-von Weizs{\"a}cker (TFW) orbital-free energies and forces by more than two orders of magnitude, but is also more accurate than MLFFs based solely on Kohn-Sham DFT, while being more efficient and less sensitive to model parameters. We apply the framework to study the structure of molten Al$_{0.88}$Si$_{0.12}$, the results suggesting no aggregation of Si atoms, in agreement with a previous Kohn-Sham study performed at an order of magnitude smaller length and time scales.Comment: 10 pages, 7 figures, 2 table