Principles of geostatistics

Matheron, G.

doi:10.2113/gsecongeo.58.8.1246

Cited by 3,895 publications

(2,118 citation statements)

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“…The machine learning method "kriging" [38] is used to create models from the training data that can predict multipole moments using molecular geometries. Here we follow the method laid out by Jones et al [58] The kriging method is given fully in earlier works [59] and so only its key concepts are covered here.…”

Section: Machine Learningmentioning

confidence: 99%

“…[27,28] In the past we have shown FFLUX to be applicable to water clusters, [29,30] methanol, [31] N-methylacetamide [32] and all amino acids [33,34] including aromatic amino acids, [35] alanine helices, [36] and carbohydrates. [37] In previous publications, we have explored the concept of transferability using the machine learning method kriging [38] for small molecules and now turn our attention toward the challenge of predicting interatomic electrostatic interaction in proteins. In such systems, polarization has proven to be an important factor in hydrogen bonding [39][40][41][42][43] and structural determination, [44][45][46] and many groups work to incorporate these effects into modern force fields.…”

Section: Introductionmentioning

confidence: 99%

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Toward amino acid typing for proteins in FFLUX

Fletcher¹,

Popelier

2016

J Comput Chem

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Continuing the development of the FFLUX, a multipolar polarizable force field driven by machine learning, we present a modern approach to atom-typing and building transferable models for predicting atomic properties in proteins. Amino acid atomic charges in a peptide chain respond to the substitution of a neighboring residue and this response can be categorized in a manner similar to atom-typing. Using a machine learning method called kriging, we are able to build predictive models for an atom that is defined, not only by its local environment, but also by its neighboring residues, for a minimal additional computational cost. We found that prediction errors were up to 11 times lower when using a model specific to the correct group of neighboring residues, with a mean prediction of $0.0015 au. This finding suggests that atoms in a force field should be defined by more than just their immediate atomic neighbors. When comparing an atom in a single alanine to an analogous atom in a deca-alanine helix, the mean difference in charge is 0.026 au. Meanwhile, the same difference between a trialanine and a deca-alanine helix is only 0.012 au. When compared to deca-alanine models, the transferable models are up to 20 times faster to train, and require significantly less ab initio calculation, providing a practical route to modeling large biological systems.

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Section: Machine Learningmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Toward amino acid typing for proteins in FFLUX

Fletcher¹,

Popelier

2016

J Comput Chem

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“…The variables with discrete values were interpolated as a probability for existence for each value of the discrete variable. Kriging-method (Matheron 1963) can be considered the best alternative for interpolating the values of habitat component variables. From the interpolation methods, kriging makes the most benefit of the whole data measured from the area (Ripley 1981).…”

Section: Interpolation Of the Habitat Component Valuesmentioning

confidence: 99%

“…After this, a model is fitted to the semi variogram. The semivariogram is a method for measuring, presenting and modelling the variation between spatial objects (Matheron 1963). It is a two-dimensional semivariance of spatial variable describing the covariance at a given distance.…”

Section: Interpolation Of the Habitat Component Valuesmentioning

confidence: 99%

Relationship between forest management planning units and spatial distribution of forest habitat components in Koli National Park.

Uuttera¹,

Hyppänen²

1997

Silva Fenn.

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This study examined the relationships between forest management planning units and patches formed by forest habitat components. The test area used was a part of Koli National Park in North Karelia, eastern Finland. Forest management planning units (i.e. forest compartments) were defined by using a traditional method of Finnish forestry which applies aerial photographs and compartmentwise field inventory. Patches of forest habitat components were divided according to subjective rules by using a chosen set of variables depicting the edaphic features and vegetation of a forest habitat. The spatial distribution of the habitat components was estimated with the kriging-interpolation based on systematically located sample plots. The comparisons of the two patch mosaics were made by using the standard tools of GIS.The results of the study show that forest compartment division does not correlate very strongly with the forest habitat pattern. On average, the mean patch size of the forest habitat components is greater and the number of these patches lower compared to forest compartment division. However, if the forest habitat component distribution had been considered, the number of the forest compartments would have at least doubled after intersection.

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“…Probably the methods used most to reduce cardinality are those based on the maximisation of spatial accuracy, or in other words, on the minimisation of the variance of the estimation error, also known as variance reduction methods. This is usually carried out in the context of geostatistical theory (Matheron, 1963(Matheron, , 1965 and most frequently by interpolation with an unknown mean, i.e. by ordinary kriging.…”

Section: Introductionmentioning

confidence: 99%

Optimal estuarine sediment monitoring network design with simulated annealing

Nunes

Caeiro²,

Cunha

et al. 2006

Journal of Environmental Management

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An objective function based on geostatistical variance reduction, constrained to the reproduction of the probability distribution functions of selected physical and chemical sediment variables, is applied to the selection of the best set of compliance monitoring stations in the Sado river estuary in Portugal. These stations were to be selected from a large set of sampling stations from a prior field campaign. Simulated annealing was chosen to solve the optimisation function model. Both the combinatorial problem structure and the resulting candidate sediment monitoring networks are discussed, and the optimal dimension and spatial distribution are proposed. An optimal network of sixty stations was obtained from an original 153-station sampling campaign. q

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Principles of geostatistics

Cited by 3,895 publications

References 0 publications

Toward amino acid typing for proteins in FFLUX

Toward amino acid typing for proteins in FFLUX

Relationship between forest management planning units and spatial distribution of forest habitat components in Koli National Park.

Optimal estuarine sediment monitoring network design with simulated annealing

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