In cryo-electron microscopy, the 3D electric potentials of an ensemble of molecules are projected along arbitrary viewing directions to yield noisy 2D images. The volume maps representing these potentials typically ex...
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We propose a general machine learning-based framework for building an accurate and widely-applicable energy functional within the framework of generalized Kohn-Sham density functional theory. To this end, we develop a...
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Recent advances in single-cell RNA sequencing technologies enable deep insights into cellular development, gene regulation, and phenotypic diversity by measuring gene expression for thousands of cells in a single expe...
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Single particle cryogenic electron microscopy (cryo-EM) is an imaging technique capable of recovering the high-resolution 3-D structure of biological macromolecules from many noisy and randomly oriented projection ima...
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We introduce a new intrinsic measure of local curvature on point-cloud data called diffusion curvature. Our measure uses the framework of diffusion maps, including the data diffusion operator, to structure point cloud...
ISBN:
(纸本)9781713871088
We introduce a new intrinsic measure of local curvature on point-cloud data called diffusion curvature. Our measure uses the framework of diffusion maps, including the data diffusion operator, to structure point cloud data and define local curvature based on the laziness of a random walk starting at a point or region of the data. We show that this laziness directly relates to volume comparison results from Riemannian geometry. We then extend this scalar curvature notion to an entire quadratic form using neural network estimations based on the diffusion map of point-cloud data. We show applications of both estimations on toy data, single-cell data and on estimating local Hessian matrices of neural network loss landscapes.
We propose a nonlocal kinetic energy density functional (KEDF) for semiconductors based on the expected asymptotic behavior of its susceptibility function. The KEDF’s kernel depends on both the electron density and t...
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We propose a nonlocal kinetic energy density functional (KEDF) for semiconductors based on the expected asymptotic behavior of its susceptibility function. The KEDF’s kernel depends on both the electron density and the reduced density gradient, with an internal parameter formally related to the material’s static dielectric constant. We determine the accuracy of the KEDF within orbital-free density functional theory (DFT) by applying it to a variety of common semiconductors. With only two adjustable parameters, the KEDF reproduces quite well the exact noninteracting KEDF (i.e., Kohn-Sham DFT) predictions of bulk moduli, equilibrium volumes, and equilibrium energies. The two parameters in our KEDF are sensitive primarily to changes in the local crystal structure (such as atomic coordination number) and exhibit good transferability between different tetrahedrally-bonded phases. This local crystal structure dependence is rationalized by considering Thomas-Fermi dielectric screening theory.
The emergence of low-cost sensing architectures for diverse modalities has made it possible to deploy sensor networks that acquire large amounts of very high-dimensional data. To cope with such a data deluge, manifold...
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We present a simpler proof of the existence of equilibria for a class of mean field games with common noise, where players interact through the conditional law given the current value of the common noise rather than i...
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Conventional density functional theory (DFT) fails for materials with strongly correlated electrons, such as late transition metal oxides. Large errors in the intra-atomic Coulomb and exchange interactions are the sou...
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Conventional density functional theory (DFT) fails for materials with strongly correlated electrons, such as late transition metal oxides. Large errors in the intra-atomic Coulomb and exchange interactions are the source of this failure. The DFT+U method has provided a means, through empirical parameters, to correct these errors. Here, we present a systematic ab initio approach in evaluating the intra-atomic Coulomb and exchange terms, U and J, respectively, in order to make the DFT+U method a fully first-principles technique. The method is based on a relationship between these terms and the Coulomb and exchange integrals evaluated in the basis of unrestricted Hartree-Fock molecular orbitals that represent localized states of the extended system. We used this ab initio scheme to evaluate U and J for chromia (Cr2O3). The resulting values are somewhat higher than those determined earlier either empirically or in constrained DFT calculations but have the advantage of originating from an ab initio theory containing exact exchange. Subsequent DFT+U calculations on chromia using the ab initio derived U and J yield properties consistent with experiment, unlike conventional DFT. Overall, the technique developed and tested in this work holds promise in enabling accurate and fully predictive DFT+U calculations of strongly correlated electron materials.
We consider the joint problem of system identification and inverse optimal control for discrete-time stochastic Linear Quadratic Regulators. We analyze finite and infinite time horizons in a partially observed setting...
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