21,505 research outputs found

    Jordan Areas and Grids

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    AbstractJordan curves can be used to represent special subsets of the Euclidean plane, either the (open) interior of the curve or the (compact) union of the interior and the curve itself. We compare the latter with other representations of compact sets using grids of points and we are able to show that knowing the length of a rectifiable curve is sufficient to translate from the grid representation to the Jordan curve

    Truncating the loop series expansion for Belief Propagation

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    Recently, M. Chertkov and V.Y. Chernyak derived an exact expression for the partition sum (normalization constant) corresponding to a graphical model, which is an expansion around the Belief Propagation solution. By adding correction terms to the BP free energy, one for each "generalized loop" in the factor graph, the exact partition sum is obtained. However, the usually enormous number of generalized loops generally prohibits summation over all correction terms. In this article we introduce Truncated Loop Series BP (TLSBP), a particular way of truncating the loop series of M. Chertkov and V.Y. Chernyak by considering generalized loops as compositions of simple loops. We analyze the performance of TLSBP in different scenarios, including the Ising model, regular random graphs and on Promedas, a large probabilistic medical diagnostic system. We show that TLSBP often improves upon the accuracy of the BP solution, at the expense of increased computation time. We also show that the performance of TLSBP strongly depends on the degree of interaction between the variables. For weak interactions, truncating the series leads to significant improvements, whereas for strong interactions it can be ineffective, even if a high number of terms is considered.Comment: 31 pages, 12 figures, submitted to Journal of Machine Learning Researc

    Hermite regularization of the Lattice Boltzmann Method for open source computational aeroacoustics

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    The lattice Boltzmann method (LBM) is emerging as a powerful engineering tool for aeroacoustic computations. However, the LBM has been shown to present accuracy and stability issues in the medium-low Mach number range, that is of interest for aeroacoustic applications. Several solutions have been proposed but often are too computationally expensive, do not retain the simplicity and the advantages typical of the LBM, or are not described well enough to be usable by the community due to proprietary software policies. We propose to use an original regularized collision operator, based on the expansion in Hermite polynomials, that greatly improves the accuracy and stability of the LBM without altering significantly its algorithm. The regularized LBM can be easily coupled with both non-reflective boundary conditions and a multi-level grid strategy, essential ingredients for aeroacoustic simulations. Excellent agreement was found between our approach and both experimental and numerical data on two different benchmarks: the laminar, unsteady flow past a 2D cylinder and the 3D turbulent jet. Finally, most of the aeroacoustic computations with LBM have been done with commercial softwares, while here the entire theoretical framework is implemented on top of an open source library (Palabos).Comment: 34 pages, 12 figures, The Journal of the Acoustical Society of America (in press

    Mapping solar array location, size, and capacity using deep learning and overhead imagery

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    The effective integration of distributed solar photovoltaic (PV) arrays into existing power grids will require access to high quality data; the location, power capacity, and energy generation of individual solar PV installations. Unfortunately, existing methods for obtaining this data are limited in their spatial resolution and completeness. We propose a general framework for accurately and cheaply mapping individual PV arrays, and their capacities, over large geographic areas. At the core of this approach is a deep learning algorithm called SolarMapper - which we make publicly available - that can automatically map PV arrays in high resolution overhead imagery. We estimate the performance of SolarMapper on a large dataset of overhead imagery across three US cities in California. We also describe a procedure for deploying SolarMapper to new geographic regions, so that it can be utilized by others. We demonstrate the effectiveness of the proposed deployment procedure by using it to map solar arrays across the entire US state of Connecticut (CT). Using these results, we demonstrate that we achieve highly accurate estimates of total installed PV capacity within each of CT's 168 municipal regions

    Water and energy footprint of irrigated agriculture in the Mediterranean region

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    Irrigated agriculture constitutes the largest consumer of freshwater in the Mediterranean region and provides a major source of income and employment for rural livelihoods. However, increasing droughts and water scarcity have highlighted concerns regarding the environmental sustainability of agriculture in the region. An integrated assessment combining a gridded water balance model with a geodatabase and GIS has been developed and used to assess the water demand and energy footprint of irrigated production in the region. Modelled outputs were linked with crop yield and water resources data to estimate water (m3 kg−1) and energy (CO2 kg−1) productivity and identify vulnerable areas or 'hotspots'. For a selected key crops in the region, irrigation accounts for 61 km3 yr−1 of water abstraction and 1.78 Gt CO2 emissions yr−1, with most emissions from sunflower (73 kg CO2/t) and cotton (60 kg CO2/t) production. Wheat is a major strategic crop in the region and was estimated to have a water productivity of 1000 t Mm−3 and emissions of 31 kg CO2/t. Irrigation modernization would save around 8 km3 of water but would correspondingly increase CO2 emissions by around +135%. Shifting from rain-fed to irrigated production would increase irrigation demand to 166 km3 yr−1 (+137%) whilst CO2 emissions would rise by +270%. The study has major policy implications for understanding the water–energy–food nexus in the region and the trade-offs between strategies to save water, reduce CO2 emissions and/or intensify food production
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