Ground state of two electrons on concentric spheres

We extend our analysis of two electrons on a sphere [Phys. Rev. A {\bf 79}, 062517 (2009); Phys. Rev. Lett. {\bf 103}, 123008 (2009)] to electrons on concentric spheres with different radii. The strengths and weaknesses of several electronic structure models are analyzed, ranging from the mean-field approximation (restricted and unrestricted Hartree-Fock solutions) to configuration interaction expansion, leading to near-exact wave functions and energies. The M{\o}ller-Plesset energy corrections (up to third-order) and the asymptotic expansion for the large-spheres regime are also considered. We also study the position intracules derived from approximate and exact wave functions. We find evidence for the existence of a long-range Coulomb hole in the large-spheres regime, and infer that unrestricted Hartree-Fock theory over-localizes the electrons.Comment: 10 pages, 10 figure

Sophisticated Inference.

Active inference offers a first principle account of sentient behavior, from which special and important cases-for example, reinforcement learning, active learning, Bayes optimal inference, Bayes optimal design-can be derived. Active inference finesses the exploitation-exploration dilemma in relation to prior preferences by placing information gain on the same footing as reward or value. In brief, active inference replaces value functions with functionals of (Bayesian) beliefs, in the form of an expected (variational) free energy. In this letter, we consider a sophisticated kind of active inference using a recursive form of expected free energy. Sophistication describes the degree to which an agent has beliefs about beliefs. We consider agents with beliefs about the counterfactual consequences of action for states of affairs and beliefs about those latent states. In other words, we move from simply considering beliefs about "what would happen if I did that" to "what I would believe about what would happen if I did that." The recursive form of the free energy functional effectively implements a deep tree search over actions and outcomes in the future. Crucially, this search is over sequences of belief states as opposed to states per se. We illustrate the competence of this scheme using numerical simulations of deep decision problems

Relevance of the slowly-varying electron gas to atoms, molecules, and solids

Under a certain scaling, the electron densities of finite systems become both large and slowly-varying, so that the gradient expansions of the density functionals for the Kohn-Sham kinetic and exchange energies become asymptotically exact to order $\nabla^2$. Neutral atoms of large $Z$ scale similarly, but a cusp correction at the nucleus requires generalizing the gradient expansion for exchange, producing the wrong gradient coefficient in the slowly-varying limit. Meta-generalized gradient approximations (meta-GGA's) recover both the slowly-varying and large-$Z$ limits. GGA correlation energies of large-Z atoms are found to be accurate.Comment: 5 pages, 4 figures, submitted at PR

Dietary Protein Deficiency and Mycobacterium Bovis BCG Affect Interleukin-2 Activity in Experimental Pulmonary Tuberculosis

Inbred strain 2 guinea pigs were vaccinated with Mycobacterium bovis BCG or were left unvaccinated. They were maintained for 6 weeks on defined, isocaloric diets containing either 30% (control animals) or 10% (animals receiving low protein) ovalbumin as the sole protein source. Animals were challenged by the respiratory route with a low dose of virulent M. tuberculosis H37Rv and killed 4 weeks later. Protein-malnourished animals were not protected by previous vaccination with BCG. Lymphocytes isolated from various tissues were tested in vitro for proliferative responses to mitogen (concanavalin A) and antigen (purified protein derivative [PPD]), production of interleukin-2 (IL-2), and response to exogenous recombinant IL-2 (rIL-2). Protein-malnourished guinea pigs responded only weakly to PPD skin tests, and their blood and lymph node lymphocytes exhibited impaired proliferation when cultured with PPD in vitro. IL-2 levels were consistently low in cultures of stimulated blood and spleen lymphocytes from protein-deprived animals. BCG vaccination of nutritionally normal guinea pigs, on the other hand, induced significantly more IL-2 production by PPD- and concanavalin A-stimulated lymphocytes. The addition of exogenous mouse rIL-2 (40 and 80 U/ml) in vitro to PPD-stimulated blood and lymph node cells from nonvaccinated, protein-deprived guinea pigs resulted in no improvement of the proliferative response. Previous vaccination of malnourished guinea pigs did not consistently enhance the response of PPD-stimulated lymphocytes to added rIL-2. Dietary protein deficiency and BCG vaccination appear to modulate antigen-driven cellular immunity in animals with tuberculosis by altering the production of, and the response to, IL-2 by PPD-stimulated lymphocytes

The experience of children with disabilities and their families during the COVID-19 pandemic; what lessons can we learn?

COVID-19 has had serious, negative impacts on children’s health and development. But the impacts have not been felt equally; disabled children and their families have been hit particularly hard. In this paper we summarise UK legislation to limit the spread of the virus and describe how services to disabled children changed as a result. We discuss the long-term deleterious impacts of changes in service provision on the health and wellbeing of disabled children and the parent carers supporting them. We close with lessons learned for resetting services to support the ongoing recovery of children and their families and recommendations for delivering services better in future emergencies to ensure that disabled children’s health and wellbeing is maintained

Density Functional Theory for the Photoionization Dynamics of Uracil

Photoionization dynamics of the RNA base Uracil is studied in the framework of Density Functional Theory (DFT). The photoionization calculations take advantage of a newly developed parallel version of a multicentric approach to the calculation of the electronic continuum spectrum which uses a set of B-spline radial basis functions and a Kohn-Sham density functional hamiltonian. Both valence and core ionizations are considered. Scattering resonances in selected single-particle ionization channels are classified by the symmetry of the resonant state and the peak energy position in the photoelectron kinetic energy scale; the present results highlight once more the site specificity of core ionization processes. We further suggest that the resonant structures previously characterized in low-energy electron collision experiments are partly shifted below threshold by the photoionization processes. A critical evaluation of the theoretical results providing a guide for future experimental work on similar biosystems

Extended Huckel theory for bandstructure, chemistry, and transport. II. Silicon

In this second paper, we develop transferable semi-empirical parameters for the technologically important material, silicon, using Extended Huckel Theory (EHT) to calculate its electronic structure. The EHT-parameters areoptimized to experimental target values of the band dispersion of bulk-silicon. We obtain a very good quantitative match to the bandstructure characteristics such as bandedges and effective masses, which are competitive with the values obtained within an $sp^3 d^5 s^*$ orthogonal-tight binding model for silicon. The transferability of the parameters is investigated applying them to different physical and chemical environments by calculating the bandstructure of two reconstructed surfaces with different orientations: Si(100) (2x1) and Si(111) (2x1). The reproduced $\pi$- and $\pi^*$-surface bands agree in part quantitatively with DFT-GW calculations and PES/IPES experiments demonstrating their robustness to environmental changes. We further apply the silicon parameters to describe the 1D band dispersion of a unrelaxed rectangular silicon nanowire (SiNW) and demonstrate the EHT-approach of surface passivation using hydrogen. Our EHT-parameters thus provide a quantitative model of bulk-silicon and silicon-based materials such as contacts and surfaces, which are essential ingredients towards a quantitative quantum transport simulation through silicon-based heterostructures.Comment: 9 pages, 9 figure

Particle-Number Restoration within the Energy Density Functional Formalism

We give a detailed analysis of the origin of spurious divergences and finite steps that have been recently identified in particle-number restoration calculations within the nuclear energy density functional framework. We isolate two distinct levels of spurious contributions to the energy. The first one is encoded in the definition of the basic energy density functional itself whereas the second one relates to the canonical procedure followed to extend the use of the energy density functional to multi-reference calculations. The first level of spuriosity relates to the long-known self-interaction problem and to the newly discussed self-pairing interaction process which might appear when describing paired systems with energy functional methods using auxiliary reference states of Bogoliubov or BCS type. A minimal correction to the second level of spuriosity to the multi-reference nuclear energy density functional proposed in [D. Lacroix, T. Duguet, M. Bender, arXiv:0809.2041] is shown to remove completely the anomalies encountered in particle-number restored calculations. In particular, it restores sum-rules over (positive) particle numbers that are to be fulfilled by the particle-number-restored formalism. The correction is found to be on the order of several hundreds of keVs up to about 1 MeV in realistic calculations, which is small compared to the total binding energy, but often accounts for a substantial percentage of the energy gain from particle-number restoration and is on the same energy scale as the excitations one addresses with multi-reference energy density functional methods.Comment: 37 pages, 14 figures, accepted for publication in PR

Human Faces Are Slower than Chimpanzee Faces

BACKGROUND: While humans (like other primates) communicate with facial expressions, the evolution of speech added a new function to the facial muscles (facial expression muscles). The evolution of speech required the development of a coordinated action between visual (movement of the lips) and auditory signals in a rhythmic fashion to produce "visemes" (visual movements of the lips that correspond to specific sounds). Visemes depend upon facial muscles to regulate shape of the lips, which themselves act as speech articulators. This movement necessitates a more controlled, sustained muscle contraction than that produced during spontaneous facial expressions which occur rapidly and last only a short period of time. Recently, it was found that human tongue musculature contains a higher proportion of slow-twitch myosin fibers than in rhesus macaques, which is related to the slower, more controlled movements of the human tongue in the production of speech. Are there similar unique, evolutionary physiologic biases found in human facial musculature related to the evolution of speech?\ud \ud METHODOLOGY/PRINICIPAL FINDINGS: Using myosin immunohistochemistry, we tested the hypothesis that human facial musculature has a higher percentage of slow-twitch myosin fibers relative to chimpanzees (Pan troglodytes) and rhesus macaques (Macaca mulatta). We sampled the orbicularis oris and zygomaticus major muscles from three cadavers of each species and compared proportions of fiber-types. Results confirmed our hypothesis: humans had the highest proportion of slow-twitch myosin fibers while chimpanzees had the highest proportion of fast-twitch fibers.\ud \ud CONCLUSIONS/SIGNIFICANCE: These findings demonstrate that the human face is slower than that of rhesus macaques and our closest living relative, the chimpanzee. They also support the assertion that human facial musculature and speech co-evolved. Further, these results suggest a unique set of evolutionary selective pressures on human facial musculature to slow down while the function of this muscle group diverged from that of other primates.\ud \u