Three mathematical models for bucking-to-order

Abstract

Robust Nonlinear Mapping of Soil Contamination Using Support Regression

Spatial data analysis mapping and visualization is of great importance in various fields: environment, pollution, natural hazards and risks, epidemiology, spatial econometrics, etc. A basic task of spatial mapping is to make predictions based on some empirical data (measurements). A number of state-of-the-art methods can be used for the task: deterministic interpolations, methods of geostatistics: the family of kriging estimators (Deutsch and Journel, 1997), machine learning algorithms such as artificial neural networks (ANN) of different architectures, hybrid ANN-geostatistics models (Kanevski and Maignan, 2004; Kanevski et al., 1996), etc. All the methods mentioned above can be used for solving the problem of spatial data mapping. Environmental empirical data are always contaminated/corrupted by noise, and often with noise of unknown nature. That's one of the reasons why deterministic models can be inconsistent, since they treat the measurements as values of some unknown function that should be interpolated. Kriging estimators treat the measurements as the realization of some spatial randomn process. To obtain the estimation with kriging one has to model the spatial structure of the data: spatial correlation function or (semi-)variogram. This task can be complicated if there is not sufficient number of measurements and variogram is sensitive to outliers and extremes. ANN is a powerful tool, but it also suffers from the number of reasons. of a special type ? multiplayer perceptrons ? are often used as a detrending tool in hybrid (ANN+geostatistics) models (Kanevski and Maignank, 2004). Therefore, development and adaptation of the method that would be nonlinear and robust to noise in measurements, would deal with the small empirical datasets and which has solid mathematical background is of great importance. The present paper deals with such model, based on Statistical Learning Theory (SLT) - Support Vector Regression. SLT is a general mathematical framework devoted to the problem of estimation of the dependencies from empirical data (Hastie et al, 2004; Vapnik, 1998). SLT models for classification - Support Vector Machines - have shown good results on different machine learning tasks. The results of SVM classification of spatial data are also promising (Kanevski et al, 2002). The properties of SVM for regression - Support Vector Regression (SVR) are less studied. First results of the application of SVR for spatial mapping of physical quantities were obtained by the authorsin for mapping of medium porosity (Kanevski et al, 1999), and for mapping of radioactively contaminated territories (Kanevski and Canu, 2000). The present paper is devoted to further understanding of the properties of SVR model for spatial data analysis and mapping. Detailed description of the SVR theory can be found in (Cristianini and Shawe-Taylor, 2000; Smola, 1996) and basic equations for the nonlinear modeling are given in section 2. Section 3 discusses the application of SVR for spatial data mapping on the real case study - soil pollution by Cs137 radionuclide. Section 4 discusses the properties of the modelapplied to noised data or data with outliers.

Metabolic fate of fructose ingested with and without glucose in a mixed meal.

Ingestion of pure fructose stimulates de novo lipogenesis and gluconeogenesis. This may however not be relevant to typical nutritional situations, where fructose is invariably ingested with glucose. We therefore assessed the metabolic fate of fructose incorporated in a mixed meal without or with glucose in eight healthy volunteers. Each participant was studied over six hours after the ingestion of liquid meals containing either 13C-labelled fructose, unlabeled glucose, lipids and protein (Fr + G) or 13C-labelled fructose, lipids and protein, but without glucose (Fr), or protein and lipids alone (ProLip). After Fr + G, plasma 13C-glucose production accounted for 19.0% ± 1.5% and 13CO2 production for 32.2% ± 1.3% of 13C-fructose carbons. After Fr, 13C-glucose production (26.5% ± 1.4%) and 13CO2 production (36.6% ± 1.9%) were higher (p < 0.05) than with Fr + G. 13C-lactate concentration and very low density lipoprotein VLDL 13C-palmitate concentrations increased to the same extent with Fr + G and Fr, while chylomicron 13C-palmitate tended to increase more with Fr + G. These data indicate that gluconeogenesis, lactic acid production and both intestinal and hepatic de novo lipogenesis contributed to the disposal of fructose carbons ingested together with a mixed meal. Co-ingestion of glucose decreased fructose oxidation and gluconeogenesis and tended to increase 13C-pamitate concentration in gut-derived chylomicrons, but not in hepatic-borne VLDL-triacylglycerol (TG). This trial was approved by clinicaltrial. gov. Identifier is NCT01792089.