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.

Comparison of aortic elasticity determined by cardiovascular magnetic resonance imaging in obese versus lean adults.

The vascular properties of large vessels in the obese have not been adequately studied. We used cardiovascular magnetic resonance imaging to quantify the cross-sectional area and elastic properties of the ascending thoracic and abdominal aorta in 21 clinically healthy obese young adult men and 25 men who were age-matched lean controls. Obese subjects had greater maximal cross-sectional area of the ascending thoracic aorta (984 +/- 252 vs 786 +/- 109 mm(2), p <0.01) and of the abdominal aorta (415 +/- 71 vs 374 +/- 51 mm(2), p <0.05). When indexed for height the differences persisted, but when indexed for body surface area, a significant difference between groups was found only for the maximal abdominal aortic cross-sectional area. The obese subjects also had decreased abdominal aortic elasticity, characterized by 24% lower compliance (0.0017 +/- 0.0004 vs 0.0021 +/- 0.0005 mm(2)/kPa/mm, p <0.01), 22% higher stiffness index beta (6.0 +/- 1.5 vs 4.9 +/- 0.7, p <0.005), and 41% greater pressure-strain elastic modulus (72 +/- 25 vs 51 +/- 9, p <0.005). At the ascending thoracic aorta, only the pressure-strain elastic modulus was different between obese and lean subjects (85 +/- 42 vs 65 +/- 26 kPa, respectively; p <0.05), corresponding to a 31% difference-but arterial compliance and stiffness index were not significantly different between groups. In clinically healthy young adult obese men, obesity is associated with increased cross-sectional aortic area and decreased aortic elasticity.

Diabetic neuropathy is a more important determinant of baroreflex sensitivity than carotid elasticity in type 2 diabetes.

The object of this study was to evaluate the contribution of carotid distensibilty on baroreflex sensitivity in patients with type 2 diabetes mellitus with at least 2 additional cardiovascular risk factors. Carotid distensibility was measured bilaterally at the common carotid artery in 79 consecutive diabetic patients and 60 matched subjects without diabetes. Spontaneous baroreflex sensitivity assessment was obtained using time and frequency methods. Baroreflex sensitivity was lower in diabetic subjects as compared with nondiabetic control subjects (5.25+/-2.80 ms/mm Hg versus 7.55+/-3.79 ms/mm Hg; P<0.01, respectively). Contrary to nondiabetic subjects, diabetic subjects showed no significant correlation between carotid distensibility and baroreflex sensitivity (r2=0.08, P=0.04 and r2=0.04, P=0.13, respectively). In diabetic subjects, baroreflex sensitivity was significantly lower in subjects with peripheral neuropathy than in those with preserved vibration sensation (4.1+/-0.5 versus 6.1+/-0.4 ms/mm Hg, respectively; P=0.005). Age in nondiabetic subjects, diabetes duration, systolic blood pressure, peripheral or sensitive neuropathy, and carotid distensibility were introduced in a stepwise multivariate analysis to identify the determinants of baroreflex sensitivity. In diabetic patients, neuropathy is a more sensitive determinant of baroreflex sensitivity than the reduced carotid distensibility (stepwise analysis; F ratio=5.1, P=0.028 versus F ratio=1.9, P=0.16, respectively). In diabetic subjects with 2 additional cardiovascular risk factors, spontaneous baroreflex sensitivity is not related to carotid distensibility. Diabetic subjects represent a particular population within the spectrum of cardiovascular risk situations because of the marked neuropathy associated with their metabolic disorder. Therefore, neuropathy is a more significant determinant of baroreflex sensitivity than carotid artery elasticity in patients with type 2 diabetes.