20,422 research outputs found

    Theory of the Magnetic Moment in Iron Pnictides

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    We show that the combined effects of spin-orbit, monoclinic distortion, and p-d hybridization in tetrahedrally coordinated Fe in LaOFeAs invalidates the naive Hund's rule filling of the Fe d-levels. The two highest occupied levels have one electron each but as a result of the p-d hybridization have very different on-site repulsions. As a result, electrons in the upper level are more itinerant while those in the lower level are more localized. It is the xy-projection of the spin in the lower level that orders antiferromagnetically as the z-components of the spins in the two levels is shown to be vanishingly small in the ground state. The resulting magnetic moment is highly anisotropic with an in-plane value of 0.250.35μB0.25-0.35\mu_B per Fe and a z-projection of 0.06μB0.06\mu_B, both of which are in agreement with experiment. As a consequence, we arrive the minimal model that describes the electronic properties of LaOFeAs.Comment: Published Versio

    Sinusoidal Modeling Applied to Spatially Variant Tropospheric Ozone Air Pollution

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    This paper demonstrates how parsimonious models of sinusoidal functions can be used to fit spatially variant time series in which there is considerable variation of a periodic type. A typical shortcoming of such tools relates to the difficulty in capturing idiosyncratic variation in periodic models. The strategy developed here addresses this deficiency. While previous work has sought to overcome the shortcoming by augmenting sinusoids with other techniques, the present approach employs station-specific sinusoids to supplement a common regional component, which succeeds in capturing local idiosyncratic behavior in a parsimonious manner. The experiments conducted herein reveal that a semi-parametric approach enables such models to fit spatially varying time series with periodic behavior in a remarkably tight fashion. The methods are applied to a panel data set consisting of hourly air pollution measurements. The augmented sinusoidal models produce an excellent fit to these data at three different levels of spatial detail.Air Pollution, Idiosyncratic component, Regional variation, Semiparametric model, Sinusoidal function, Spatial-temporal data, Tropospheric Ozone

    Solving Tree Problems with Category Theory

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    Artificial Intelligence (AI) has long pursued models, theories, and techniques to imbue machines with human-like general intelligence. Yet even the currently predominant data-driven approaches in AI seem to be lacking humans' unique ability to solve wide ranges of problems. This situation begs the question of the existence of principles that underlie general problem-solving capabilities. We approach this question through the mathematical formulation of analogies across different problems and solutions. We focus in particular on problems that could be represented as tree-like structures. Most importantly, we adopt a category-theoretic approach in formalising tree problems as categories, and in proving the existence of equivalences across apparently unrelated problem domains. We prove the existence of a functor between the category of tree problems and the category of solutions. We also provide a weaker version of the functor by quantifying equivalences of problem categories using a metric on tree problems.Comment: 10 pages, 4 figures, International Conference on Artificial General Intelligence (AGI) 201
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