706 research outputs found

    ChatGPT and Excel -- trust, but verify

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    This paper adopts a critical approach to ChatGPT, showing how its huge reach makes it a useful tool for people with simple requirements but a bad, even misleading guide to those with more complex problems which are more rarely present in the training data and even more rarely have straightforward solutions. It works through four exercises in creating lookup formulas using chatbots, showing the need to test the offered solutions. They are a simple lookup, a lookup to the left, a match of two values at the same time, and intentionally confusing the models by using common language with technical meaning in Excel. It concludes with a practical guide for how to add an Excelscript button, with system and user prompts, to the ChatGPT API into the Excel desktop environment, supported by a blog post giving the technical details for those interested.Comment: 15 pages, 3 figure

    Constraining alternative theories of gravity using pulsar timing arrays

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    The opening of the gravitational wave window by ground-based laser interferometers has made possible many new tests of gravity, including the first constraints on polarization. It is hoped that within the next decade pulsar timing will extend the window by making the first detections in the nano-Hertz frequency regime. Pulsar timing offers several advantages over ground-based interferometers for constraining the polarization of gravitational waves due to the many projections of the polarization pattern provided by the different lines of sight to the pulsars, and the enhanced response to longitudinal polarizations. Here we show that existing results from pulsar timing arrays can be used to place stringent limits on the energy density of longitudinal stochastic gravitational waves. Paradoxically however, we find that longitudinal modes will be very difficult to detect due to the large variance in the pulsar-pulsar correlation patterns for these modes. Existing upper limits on the power spectrum of pulsar timing residuals imply that the amplitude of vector longitudinal and scalar longitudinal modes at frequencies of 1/year are constrained: AVL<4.1×10−16{\cal A}_{\rm VL} < 4.1\times 10^{-16} and ASL<3.7×10−17{\cal A}_{\rm SL} < 3.7\times 10^{-17}, while the bounds on the energy density for a scale invariant cosmological background are: ΩVLh2<3.5×10−11\Omega_{\rm VL}h^2 < 3.5 \times 10^{-11} and ΩSLh2<3.2×10−13\Omega_{\rm SL}h^2 < 3.2 \times 10^{-13}.Comment: 5 pages, 4 figure

    Using evidence in the classroom : what works and why?

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