21,505 research outputs found
Jordan Areas and Grids
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
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
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
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
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
- …