Distribution of distance in the spheroid

Garcı́a-Pelayo, Ricardo

doi:10.1088/0305-4470/38/16/001

Cited by 34 publications

(19 citation statements)

References 13 publications

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“…For example, average household distance to an affected resource would be a monotonic function of market area for a circular market with the affected resource at the centroid, and population randomly distributed. Similar relationships hold for other distance measures and bounded shapes, as established by the theory of distance in bounded areas (García-Pelayo 2005). Finally, the expected economic value of environmental quality change is often related to the availability of proximate substitutes and complements (Ghermandi and Nunes 2013;Johnston et al 2002b;Schaafsma 2015;Schaafsma et al 2012).…”

Section: Geospatial Variables In Meta-analysis and Benefit Transfermentioning

confidence: 75%

Enhanced Geospatial Validity for Meta-analysis and Environmental Benefit Transfer: An Application to Water Quality Improvements

Johnston

Besedin

Stapler

2016

Environ Resource Econ

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Meta-regression models are commonly used within benefit transfer to estimate willingness to pay (WTP) for environmental quality improvements. Theory suggests that these estimates should be sensitive to geospatial factors including resource scale, market extent, and the availability of substitutes and complements. Valuation meta-regression models addressing the quantity of non-market commodities sometimes incorporate spatial variables that proxy for a subset of these effects. However, meta-analyses of WTP for environmental quality generally omit geospatial factors such as these, leading to benefit transfers that are invariant to these factors. This paper reports on a meta-regression model for water quality benefit transfer that incorporates spatially explicit factors predicted by theory to influence WTP. The metadata are drawn from stated preference studies that estimate per household WTP for water quality changes in United States water bodies, and combine primary study information with extensive geospatial data from external sources. Results find that geospatial variables are associated with significant WTP variations as predicted by theory, and that inclusion of these variables reduces transfer errors.

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Section: Geospatial Variables In Meta-analysis and Benefit Transfermentioning

confidence: 75%

Enhanced Geospatial Validity for Meta-analysis and Environmental Benefit Transfer: An Application to Water Quality Improvements

Johnston

Besedin

Stapler

2016

Environ Resource Econ

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“…According to Equation 3, in a reference state with uncorrelated positions of atoms i and j [i.e., pðx i ;x j Þ ¼ pðx i Þpðx j Þ], the normalization function nðr; aÞ is equal to the distance pdf p REF m;n ðr; aÞ. Although p REF m;n ðr; aÞ and nðr; aÞ for a sphere have already been calculated (Deltheli 1919;Hammersley 1950;Lord 1954;de Smith 1977;Tu and Fischbach 2002;Garcia-Pelayo 2005), we re-derive them here for completeness.…”

Section: Theorymentioning

confidence: 99%

Statistical potential for assessment and prediction of protein structures

2006

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Protein structures in the Protein Data Bank provide a wealth of data about the interactions that determine the native states of proteins. Using the probability theory, we derive an atomic distancedependent statistical potential from a sample of native structures that does not depend on any adjustable parameters (Discrete Optimized Protein Energy, or DOPE). DOPE is based on an improved reference state that corresponds to noninteracting atoms in a homogeneous sphere with the radius dependent on a sample native structure; it thus accounts for the finite and spherical shape of the native structures. The DOPE potential was extracted from a nonredundant set of 1472 crystallographic structures. We tested DOPE and five other scoring functions by the detection of the native state among six multiple target decoy sets, the correlation between the score and model error, and the identification of the most accurate non-native structure in the decoy set. For all decoy sets, DOPE is the best performing function in terms of all criteria, except for a tie in one criterion for one decoy set. To facilitate its use in various applications, such as model assessment, loop modeling, and fitting into cryo-electron microscopy mass density maps combined with comparative protein structure modeling, DOPE was incorporated into the modeling package MODELLER-8.

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“…and 6 = 17 126 · 3 1/2 + 3 73 3150 · 3 1/2 + 31 1050 · 3 1/2 + 9 70 · 3 1/2 = 664 1575 · 3 1/2 ≈ 0.243404.…”

Section: B Example: the Equilateral Triangleunclassified

Moments of the distribution of distance

Garcı́a-Pelayo

2011

Journal of Mathematical Physics

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It is shown that the even moments of the distribution of distance of a density are polynomials of the moments of that density. It is discussed when the even moments alone determine the distribution of distance. Examples are computed explicitly. It follows that moments of the lengths of chords and other quantities treated in geometric probability can also be computed in terms of the moments of the density. These formulas are collected here. The formalism is not restricted to homogeneous densities on bounded support (“bodies”). As an example, the distributions of distance of the isotropic Gaussian and of the Cantor set are computed.

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Distribution of distance in the spheroid

Cited by 34 publications

References 13 publications

Enhanced Geospatial Validity for Meta-analysis and Environmental Benefit Transfer: An Application to Water Quality Improvements

Enhanced Geospatial Validity for Meta-analysis and Environmental Benefit Transfer: An Application to Water Quality Improvements

Statistical potential for assessment and prediction of protein structures

Moments of the distribution of distance

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