High-density correlation energy expansion of the one-dimensional uniform electron gas

We show that the expression of the high-density (i.e small-$r_s$) correlation energy per electron for the one-dimensional uniform electron gas can be obtained by conventional perturbation theory and is of the form \Ec(r_s) = -\pi^2/360 + 0.00845 r_s + ..., where $r_s$ is the average radius of an electron. Combining these new results with the low-density correlation energy expansion, we propose a local-density approximation correlation functional, which deviates by a maximum of 0.1 millihartree compared to the benchmark DMC calculations.Comment: 7 pages, 2 figures, 3 tables, accepted for publication in J. Chem. Phy

Bands, resonances, edge singularities and excitons in core level spectroscopy investigated within the dynamical mean field theory

Using a recently developed impurity solver we exemplify how dynamical mean field theory captures band excitations, resonances, edge singularities and excitons in core level x-ray absorption (XAS) and core level photo electron spectroscopy (cPES) on metals, correlated metals and Mott insulators. Comparing XAS at different values of the core-valence interaction shows how the quasiparticle peak in the absence of core-valence interactions evolves into a resonance of similar shape, but different origin. Whereas XAS is rather insensitive to the metal insulator transition, cPES can be used, due to nonlocal screening, to measure the amount of local charge fluctuation

Bayesian estimation of orientation preference maps

Imaging techniques such as optical imaging of intrinsic signals, 2-photon calcium imaging and voltage sensitive dye imaging can be used to measure the functional organization of visual cortex across different spatial and temporal scales. Here, we present Bayesian methods based on Gaussian processes for extracting topographic maps from functional imaging data. In particular, we focus on the estimation of orientation preference maps (OPMs) from intrinsic signal imaging data. We model the underlying map as a bivariate Gaussian process, with a prior covariance function that reflects known properties of OPMs, and a noise covariance adjusted to the data. The posterior mean can be interpreted as an optimally smoothed estimate of the map, and can be used for model based interpolations of the map from sparse measurements. By sampling from the posterior distribution, we can get error bars on statistical properties such as preferred orientations, pinwheel locations or pinwheel counts. Finally, the use of an explicit probabilistic model facilitates interpretation of parameters and quantitative model comparisons. We demonstrate our model both on simulated data and on intrinsic signaling data from ferret visual cortex

Training deep neural density estimators to identify mechanistic models of neural dynamics

Mechanistic modeling in neuroscience aims to explain observed phenomena in terms of underlying causes. However, determining which model parameters agree with complex and stochastic neural data presents a significant challenge. We address this challenge with a machine learning tool which uses deep neural density estimators-- trained using model simulations-- to carry out Bayesian inference and retrieve the full space of parameters compatible with raw data or selected data features. Our method is scalable in parameters and data features, and can rapidly analyze new data after initial training. We demonstrate the power and flexibility of our approach on receptive fields, ion channels, and Hodgkin-Huxley models. We also characterize the space of circuit configurations giving rise to rhythmic activity in the crustacean stomatogastric ganglion, and use these results to derive hypotheses for underlying compensation mechanisms. Our approach will help close the gap between data-driven and theory-driven models of neural dynamics

Electronic depth profiles with atomic layer resolution from resonant soft x-ray reflectivity

The analysis of x-ray reflectivity data from artificial heterostructures usually relies on the homogeneity of optical properties of the constituent materials. However, when the x-ray energy is tuned to an absorption edge, this homogeneity no longer exists. Within the same material, spatial regions containing elements at resonance will have optical properties very different from regions without resonating sites. In this situation, models assuming homogeneous optical properties throughout the material can fail to describe the reflectivity adequately. As we show here, resonant soft x-ray reflectivity is sensitive to these variations, even though the wavelength is typically large as compared to the atomic distances over which the optical properties vary. We have therefore developed a scheme for analyzing resonant soft x-ray reflectivity data, which takes the atomic structure of a material into account by "slicing" it into atomic planes with characteristic optical properties. Using LaSrMnO4 as an example, we discuss both the theoretical and experimental implications of this approach. Our analysis not only allows to determine important structural information such as interface terminations and stacking of atomic layers, but also enables to extract depth-resolved spectroscopic information with atomic resolution, thus enhancing the capability of the technique to study emergent phenomena at surfaces and interfaces.Comment: Completely overhauled with respect to the previous version due to peer revie

The role of ice particle shapes and size distributions in the single scattering properties of cirrus clouds

The roles of ice particle size distributions (SDs) and particle shapes in cirrus cloud solar radiative transfer are investigated by analyzing SDs obtained from optical array probe measurements (particle sizes larger than 20–40 μm) during intensive field observations of the International Cirrus Experiment, the European Cloud and Radiation Experiment, the First ISCCP Regional Experiment, and the Central Equatorial Pacific Experiment. It is found that the cloud volume extinction coefficient is more strongly correlated with the total number density than with the effective particle size. Distribution-averaged mean single scattering properties are calculated for hexagonal columns, hexagonal plates, and polycrystals at a nonabsorbing (0.5 μm), moderately absorbing (1.6 μm), and strongly absorbing (3.0 μm) wavelength. At 0.5 μm (1.6 μm) (3.0 μm), the spread in the resulting mean asymmetry parameters due to different SDs is smaller than (comparable to) (smaller than) the difference caused by applying different particle shapes to these distributions. From a broadband solar radiative transfer point of view it appears more important to use the correct particle shapes than to average over the correct size distributions

Quantitative determination of bond order and lattice distortions in nickel oxide heterostructures by resonant x-ray scattering

We present a combined study of Ni $K$-edge resonant x-ray scattering and density functional calculations to probe and distinguish electronically driven ordering and lattice distortions in nickelate heterostructures. We demonstrate that due to the low crystal symmetry, contributions from structural distortions can contribute significantly to the energy-dependent Bragg peak intensities of a bond-ordered NdNiO$_3$ reference film. For a LaNiO$_3$-LaAlO$_3$ superlattice that exhibits magnetic order, we establish a rigorous upper bound on the bond-order parameter. We thus conclusively confirm predictions of a dominant spin density wave order parameter in metallic nickelates with a quasi-two-dimensional electronic structure

Solar radiative transfer simulations in Saharan dust plumes: particle shapes and 3-D effect

Radiative fields of three-dimensional inhomogeneous Saharan dust clouds have been calculated at solar wavelength (0.6 μm) by means of a Monte Carlo radiative transfer model. Scattering properties are taken from measurements in the SAMUM campaigns, from light scattering calculations for spheroids based on the MIESCHKA code, from Mie theory for spheres and from the geometric optics method assuming irregular shaped particles. Optical properties of different projected area equivalent shapes are compared. Large differences in optical properties are found especially in the phase functions. Results of radiative transfer calculations based on the Monte Carlo method are shown exemplarily for one dust cloud simulated by the cloud resolving atmospheric circulation model LM-MUSCAT-DES. Shape-induced differences in the radiation fluxes are pronounced, for example, the domain averaged normalized radiance is about 30% lower in the case of a dust plume consisting of spheroids or irregular particles compared to spheres. The effect of net horizontal photon transport (3-D effect) on the reflected radiance fields is only notable at the largest gradients in optical thickness. For example, the reflectance at low sun position differs locally about 15% when horizontal photon transport is accounted for. ‘Sharp edges' due to 1-D calculations are smoothed out in the 3-D case