On ANOVA Decompositions of Kernels and Gaussian Random Field Paths

The FANOVA (or “Sobol’-Hoeffding”) decomposition of multivariate functions has been used for high-dimensional model representation and global sensitivity analysis. When the objective function f has no simple analytic form and is costly to evaluate, computing FANOVA terms may be unaffordable due to numerical integration costs. Several approximate approaches relying on Gaussian random field (GRF) models have been proposed to alleviate these costs, where f is substituted by a (kriging) predictor or by conditional simulations. Here we focus on FANOVA decompositions of GRF sample paths, and we notably introduce an associated kernel decomposition into 4 d 4d terms called KANOVA. An interpretation in terms of tensor product projections is obtained, and it is shown that projected kernels control both the sparsity of GRF sample paths and the dependence structure between FANOVA effects. Applications on simulated data show the relevance of the approach for designing new classes of covariance kernels dedicated to high-dimensional kriging.

Sediment and organic matter properties, and molecular formula from sampling locations in the Northern Black Sea

Remineralization of organic matter in reactive marine sediments releases nutrients and dissolved organic matter (DOM) into the ocean. Here we focused on the molecular-level characterization of DOM by high-resolution Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR-MS) in sediment pore waters and bottom waters from contrasting redox regimes in the northern Black Sea with particular emphasis on nitrogen-bearing compounds to derive an improved understanding of the molecular transformations involved in nitrogen release. The number of nitrogen-bearing molecules is generally higher in pore waters than in bottom waters. This suggests intensified degradation of nitrogen-bearing precursor molecules such as proteins in anoxic sediments: No significant difference was observed between sediments deposited under oxic vs anoxic conditions (average O/C ratios of 0.55) suggesting that the different organic matter quality induced by contrasting redox conditions does not impact protein diagenesis in the subseafloor. Compounds in the pore waters were on average larger, less oxygenated, and had a higher number of unsaturations. Applying a mathematical model, we could show that the assemblages of nitrogen-bearing molecular formulas are potential products of proteinaceous material that was transformed by the following reactions: (a) hydrolysis and deamination, both reducing the molecular size and nitrogen content of the products and intermediates; (b) oxidation and hydration of the intermediates; and (c) methylation and dehydration.

The expanding soybean meal market : how changes in feeding practices and growth of the formula feed industry have affected demand /

Cover title.

A formula for a better way of life; an informal chat with you ... A business man tells how he does it.

Mode of access: Internet.

The truth about choosing medical treatments : amazing secret formula.

Mode of access: Internet.

Introduction aux cours de construction : Étude et rédaction des projets. Notions succinctes sur le levé des plans, le nivellement, la cubature des terrasses et le mouvement des terres /

First published in 1867.

Algorithms for sparse Gaussian elimination with partial pivoting /

Bibliography: p. 17.

Gaussian elimination and numerical instability /

"UILU-ENG 77 1714."

Deposition and washout computations based on the generalized Gaussian plume model /

"September 30, 1963."

A formula book of English official historical documents.

pt. 1. Diplomatic documents selected and transcribed by a seminar of the London School of Economics.--pt. 2. Ministerial and judicial records selected and transcribed by a seminar of the London School of Economics.

Formula congregationis provincialis : plurium congregationum generalium, ac postremo duodecimae auctoritate probata [et] aucta.

Mode of access: Internet.

Formula congregationis procuratorum : plurium congregationum generalium, ac postremo duodecimae auctoritate probata [et] aucta.

Mode of access: Internet.

[Stoicheiosis tes christianon pisteos, e katechismos. Touto nyn prosetethe katechismos allos syntomoteros. ... Elementaria traditio christianorum fidei, aut Catechismus. Huic nunc appositus est Catechismus alius magis compendiarius, & ecclesiasticarum precum formula. Omnia e Graeco in Latinum sermonem conuersa ... /

Tit. y pie de imprenta deducidos de ejemplares del ICCU y del COPAC.

Molecular formula list of compounds, names, and references to published infrared spectra; an index to 43,500 published infrared spectra. /

Accompanied by "First supplement." (iv, 112 p. 28 cm.) Published: Philadelphia [c1963]--ASTM special publication no. 333A.

Philotinus Anticyranus virum sui anicissimum Patrum Morata ... eius dissertationem publico iudico offert ... : Accedit formula de circuli quadratura.

Mode of access: Internet.