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.

MRS glucose mapping and PET joining forces: re-evaluation of the lumped constant in the rat brain under isoflurane anaesthesia.

Although numerous positron emission tomography (PET) studies with (18) F-fluoro-deoxyglucose (FDG) have reported quantitative results on cerebral glucose kinetics and consumption, there is a large variation between the absolute values found in the literature. One of the underlying causes is the inconsistent use of the lumped constants (LCs), the derivation of which is often based on multiple assumptions that render absolute numbers imprecise and errors hard to quantify. We combined a kinetic FDG-PET study with magnetic resonance spectroscopic imaging (MRSI) of glucose dynamics in Sprague-Dawley rats to obtain a more comprehensive view of brain glucose kinetics and determine a reliable value for the LC under isoflurane anaesthesia. Maps of Tmax /CMRglc derived from MRSI data and Tmax determined from PET kinetic modelling allowed to obtain an LC-independent CMRglc . The LC was estimated to range from 0.33 ± 0.07 in retrosplenial cortex to 0.44 ± 0.05 in hippocampus, yielding CMRglc between 62 ± 14 and 54 ± 11 μmol/min/100 g, respectively. These newly determined LCs for four distinct areas in the rat brain under isoflurane anaesthesia provide means of comparing the growing amount of FDG-PET data available from translational studies.

Interest rates mapping

The present study deals with the analysis and mapping of Swiss franc interest rates. Interest rates depend on time and maturity, defining term structure of the interest rate curves (IRC). In the present study IRC are considered in a two-dimensional feature space - time and maturity. Exploratory data analysis includes a variety of tools widely used in econophysics and geostatistics. Geostatistical models and machine learning algorithms (multilayer perceptron and Support Vector Machines) were applied to produce interest rate maps. IR maps can be used for the visualisation and pattern perception purposes, to develop and to explore economical hypotheses, to produce dynamic asset-liability simulations and for financial risk assessments. The feasibility of an application of interest rates mapping approach for the IRC forecasting is considered as well. (C) 2008 Elsevier B.V. All rights reserved.

Preoperative upper gastrointestinal testing can help predicting long-term outcome after gastric banding for morbid obesity.

BACKGROUND: Gastric banding (GB) is one of the most popular bariatric procedures for morbid obesity. Apart from causing weight loss by alimentary restriction, it can interfere with functions of the esophagus and upper stomach. The aim of this study was to evaluate if the results of extensive preoperative upper GI testing were correlated with long-term outcome and complications after GB. METHODS: Using a prospectively maintained computerized database including all the patients undergoing bariatric operations in both our hospitals, we performed a retrospective analysis of the patients who underwent complete upper gastrointestinal (GI) testing (endoscopy, pH monitoring, and manometry) before GB. RESULTS: One hundred thirty-four patients underwent complete testing before GB. Abnormal pH monitoring (increased total reflux time, increased diurnal reflux time, increased number of reflux episodes) predicted the development of complications and especially pouch dilatation and food intolerance. The mean De Meester score was higher among patients who developed complications than in the remaining ones (25.4 vs 17.7, P=0.03). High lower esophageal sphincter pressure also predicted progressive long-term food intolerance. Endoscopic findings were not predictive of the long-term outcome. CONCLUSIONS: There is some association between the function of the upper digestive tract and long-term complications after gastric banding. Abnormal pH monitoring predicts overall long-term complications, especially food intolerance with or without reflux, and pouch dilatation, and a high lower esophageal sphincter pressure predicts long-term food intolerance. Extended upper gastrointestinal testing with endoscopy, 24-h pH monitoring, and esophageal manometry is probably worthwhile in selecting patients for gastric banding.

Importance of abiotic stress as a range-limit determinant for European plants: insights from species' responses to climatic gradients

Aim We examined whether species occurrences are primarily limited by physiological tolerance in the abiotically more stressful end of climatic gradients (the asymmetric abiotic stress limitation (AASL) hypothesis) and the geographical predictions of this hypothesis: abiotic stress mainly determines upper-latitudinal and upper-altitudinal species range limits, and the importance of abiotic stress for these range limits increases the further northwards and upwards a species occurs. Location Europe and the Swiss Alps. Methods The AASL hypothesis predicts that species have skewed responses to climatic gradients, with a steep decline towards the more stressful conditions. Based on presence-absence data we examined the shape of plant species responses (measured as probability of occurrence) along three climatic gradients across latitudes in Europe (1577 species) and altitudes in the Swiss Alps (284 species) using Huisman-Olff-Fresco, generalized linear and generalized additive models. Results We found that almost half of the species from Europe and one-third from the Swiss Alps showed responses consistent with the predictions of the AASL hypothesis. Cold temperatures and a short growing season seemed to determine the upper-latitudinal and upper-altitudinal range limits of up to one-third of the species, while drought provided an important constraint at lower-latitudinal range limits for up to one-fifth of the species. We found a biome-dependent influence of abiotic stress and no clear support for abiotic stress as a stronger upper range-limit determinant for species with higher latitudinal and altitudinal distributions. However, the overall influence of climate as a range-limit determinant increased with latitude. Main conclusions Our results support the AASL hypothesis for almost half of the studied species, and suggest that temperature-related stress controls the upper-latitudinal and upper-altitudinal range limits of a large proportion of these species, while other factors including drought stress may be important at the lower range limits.

Structure and kinematics of the Siviez-Mischabel nappe in the Mattertal (western Alps of Switzerland) = Structure et cinématique de la nappe de Siviez-Mischabel le long de la vallée de Zermatt (Alpes de Suisse occidentale)

Résumé Cette étude porte sur le flanc inverse de la nappe de Siviez-Mischabel et sur les unités tectoniques sous jacentes (zone de Stalden supérieur et zone Houillère) dans la vallée menant à Zermatt. L'étude structurale du granite permien de Randa (orthogneiss oeillé) permet de mieux comprendre les effets de la déformation alpine sur les roches de socle. La cartographie détaillée de l'orthogneiss et de son encaissant, ainsi que l'étude lithostratigraphique des terrains sédimentaires associés permettent de proposer un schéma structural et cinématique du flanc inverse de la nappe de Siviez-Mischabel et de mieux comprendre ses relations avec les unités tectoniques sous-jacentes. L'analyse structurale de l'orthogneiss de Randa et de son encaissant révèle la superposition de plusieurs phases de déformation ductile. Cet orthogneiss formé sous des conditions métamorphiques du faciès schiste vert possède une forte schistosité alpine avec au moins deux linéations d'extension. La première, L1, orientée NW-SE est associée à la mise en place de la nappe. La seconde, L2, orientée SW-NE, se corrèle au cisaillement ductile du Simplon. La quantification de la déformation au moyen de la méthode de Fry sur les faciès porphyriques donne des ellipses à rapports axiaux compris entre 1.9 et 5.3, en accord avec les valeurs obtenues par d'autres marqueurs {tourmalines étirées, fibres). Les valeurs mesurées parallèlement à L1 ou L2 sont très semblables. La méthode de Fry a nécessité une étude théorique préalable afin de vérifier son applicabilité aux orthogneiss oeillés. La méthode requiert une distribution spatiale homogène et isotrope des marqueurs utilisés. Les tests statistiques effectués ont révélé que les phénocristaux de feldspath alcalin satisfont à cette condition et qu'ils peuvent être utilisés comme marqueur de la déformation au moyen de la méthode de Fry. Les valeurs obtenues révèlent l'importance du cisaillement ductile du Simplon sur la géométrie de la nappe dans la région d'étude. Le levé cartographique a permis d'améliorer la lithostratigraphie de la base de la nappe de Siviez-Mischabel. Trois formations en position renversée peuvent être observées sous les gneiss formant le coeur de la nappe. Ces trois formations forment le coeur du synclinal de St-Niklaus qui connecte la nappe de Siviez-Mischabel à la zone de Stalden supérieur. La datation par U-Pb de zircons détritiques et magmatiques par LA-ICP-MS permet de contraindre l'âge des formations observées (probablement Carbonifère à Trias précoce). Ces données ont des répercussions importantes sur la structure de la nappe dans la région, prouvant l'existence de plusieurs plis avec des séries normales et renversées bien préservées. La définition et la datation de ces formations, ainsi que leur identification dans la-Zone- Houillère avoisinante permettent de mieux comprendre la géométrie initiale et les relations tectoniques des nappes du Pennique moyen dans la vallée de Zermatt. Summary This study investigates the overturned limb of the Siviez-Mischabel nappe and underlying tectonic units (Upper Stalden zone and Houillère zone) in the Mattertal area. Detailed structural analysis in the Permian Randa granite (augen orthogneiss) allows a better understanding of the Alpine deformation effects on basement rocks. Detailed mapping of this orthogneiss and surrounding rocks, and the study of the lithostratigraphy in the related sedimentary horizons allow the proposition of a structural and kinematic model for the overturned limb of the Siviez-Mischabel and to better understand the relations with the underlying tectonic units. The structural analysis of the Randa orthogneiss and surrounding rocks revealed the superposition of several phases of ductile deformation. This orthogneiss formed under greenschist facies metamorphic conditions displays a strong Alpine foliation with at least two stretching lineations. The first lineation, L1, is oriented NW-SE and is related to the nappe emplacement northward. The second one, L2, is related to the Simplon ductile shear zone. Strain estimation using the Fry method has been performed on porphyritic facies of the Randa orthogneiss. The obtained ellipses have axial ratios varying between 1.9 and 5.3, in agreement with strain estimation obtained from other markers (stretched turmalines, fringes). The strain values are very similar if measured parallel to L1 or to L2. A theoretical approach was necessary to verify the relevant application of the Fry method to augen orthogneiss. This method requires that the distribution of the used markers has to be homogeneous and isotropic. Statistical tests have been done and revealed that K-feldspar phenocrysts satisfy these conditions and can be used as strain markers with the Fry method. The obtained strain measurements revealed the importance of the Simplon ductile shear zone on the geometry of the nappe in the studied area. Mapping has improved the lithostratigraphy at the base of the Siviez-Mischabel nappe. Three overturned formations can be observed below the gneisses forming the core of the nappe. These three formations form the St-Niklaus syncline, which connects the Siviez-Mischabel nappe to the underlying Upper Stalden zone. U-Pb dating of detrital and magmatic zircons by LA-ICPMS allowed the age of the observed formations to be constrained (presumably Carboniferous to Early Triassic). This data has critical implications for nappe structure in the region, composed of few recumbent folds with well preserved normal and overturned limbs. The definition and dating of these formations, as well as their identification in the adjacent "Houillère Zone" improve the understanding of the geometry and tectonic relations of the Middle Penninic nappes in the Mattertal.

Construction mechanisms and thermal evolution of upper crustal intrusions : the Saint-Jean-du-Doigt bimodal intrusion (Brittany, France)

Understanding the emplacement and growth of intrusive bodies in terms of mechanism, duration, ther¬mal evolution and rates are fundamental aspects of crustal evolution. Recent studies show that many plutons grow in several Ma by in situ accretion of discrete magma pulses, which constitute small-scale magmatic reservoirs. The residence time of magmas, and hence their capacities to interact and differentiate, are con¬trolled by the local thermal environment. The latter is highly dependant on 1) the emplacement depth, 2) the magmas and country rock composition, 3) the country rock thermal conductivity, 4) the rate of magma injection and 5) the geometry of the intrusion. In shallow level plutons, where magmas solidify quickly, evi¬dence for magma mixing and/or differentiation processes is considered by many authors to be inherited from deeper levels. This work shows however that in-situ differentiation and magma interactions occurred within basaltic and felsic sills at shallow depth (0.3 GPa) in the St-Jean-du-Doigt (SJDD) bimodal intrusion, France. This intrusion emplaced ca. 347 Ma ago (IDTIMS U/Pb on zircon) in the Precambrian crust of the Armori- can massif and preserves remarkable sill-like emplacement processes of bimodal mafic-felsic magmas. Field evidence coupled to high precision zircon U-Pb dating document progressive thermal maturation within the incrementally built ioppolith. Early m-thick mafic sills (eastern part) form the roof of the intrusion and are homogeneous and fine-grained with planar contacts with neighboring felsic sills; within a minimal 0.8 Ma time span, the system gets warmer (western part). Sills are emplaced by under-accretion under the old east¬ern part, interact and mingle. A striking feature of this younger, warmer part is in-situ differentiation of the mafic sills in the top 40 cm of the layer, which suggests liquids survival in the shallow crust. Rheological and thermal models were performed in order to determine the parameters required to allow this observed in- situ differentiation-accumulation processes. Strong constraints such as total emplacement durations (ca. 0.8 Ma, TIMS date) and pluton thickness (1.5 Km, gravity model) allow a quantitative estimation of the various parameters required (injection rates, incubation time,...). The results show that in-situ differentiation may be achieved in less than 10 years at such shallow depth, provided that: (1) The differentiating sills are injected beneath consolidated, yet still warm basalt sills, which act as low conductive insulating screens (eastern part formation in the SJDD intrusion). The latter are emplaced in a very short time (800 years) at high injection rate (0.5 m/y) in order to create a "hot zone" in the shallow crust (incubation time). This implies that nearly 1/3 of the pluton (400m) is emplaced by a subsequent and sustained magmatic activity occurring on a short time scale at the very beginning of the system. (2) Once incubation time is achieved, the calculations show that a small hot zone is created at the base of the sill pile, where new injections stay above their solidus T°C and may interact and differentiate. Extraction of differentiated residual liquids might eventually take place and mix with newly injected magma as documented in active syn-emplacement shear-zones within the "warm" part of the pluton. (3) Finally, the model show that in order to maintain a permanent hot zone at shallow level, injection rate must be of 0.03 m/y with injection of 5m thick basaltic sills eveiy 130yr, imply¬ing formation of a 15 km thick pluton. As this thickness is in contradiction with the one calculated for SJDD (1.5 Km) and exceed much the average thickness observed for many shallow level plutons, I infer that there is no permanent hot zone (or magma chambers) at such shallow level. I rather propose formation of small, ephemeral (10-15yr) reservoirs, which represent only small portions of the final size of the pluton. Thermal calculations show that, in the case of SJDD, 5m thick basaltic sills emplaced every 1500 y, allow formation of such ephemeral reservoirs. The latter are formed by several sills, which are in a mushy state and may interact and differentiate during a short time.The mineralogical, chemical and isotopic data presented in this study suggest a signature intermediate be¬tween E-MORB- and arc-like for the SJDD mafic sills and feeder dykes. The mantle source involved produced hydrated magmas and may be astenosphere modified by "arc-type" components, probably related to a sub¬ducting slab. Combined fluid mobile/immobile trace elements and Sr-Nd isotopes suggest that such subduc¬tion components are mainly fluids derived from altered oceanic crust with minor effect from the subducted sediments. Close match between the SJDD compositions and BABB may point to a continental back-arc setting with little crustal contamination. If so, the SjDD intrusion is a major witness of an extensional tectonic regime during the Early-Carboniferous, linked to the subduction of the Rheno-Hercynian Ocean beneath the Variscan terranes. Also of interest is the unusual association of cogenetic (same isotopic compositions) K-feldspar A- type granite and albite-granite. A-type granites may form by magma mixing between the mafic magma and crustal melts. Alternatively, they might derive from the melting of a biotite-bearing quartz-feldspathic crustal protolith triggered by early mafic injections at low crustal levels. Albite-granite may form by plagioclase cu¬mulate remelting issued from A-type magma differentiation.

Quantitative multi-parameter mapping of R1, PD(*), MT, and R2(*) at 3T: a multi-center validation.

Multi-center studies using magnetic resonance imaging facilitate studying small effect sizes, global population variance and rare diseases. The reliability and sensitivity of these multi-center studies crucially depend on the comparability of the data generated at different sites and time points. The level of inter-site comparability is still controversial for conventional anatomical T1-weighted MRI data. Quantitative multi-parameter mapping (MPM) was designed to provide MR parameter measures that are comparable across sites and time points, i.e., 1 mm high-resolution maps of the longitudinal relaxation rate (R1 = 1/T1), effective proton density (PD(*)), magnetization transfer saturation (MT) and effective transverse relaxation rate (R2(*) = 1/T2(*)). MPM was validated at 3T for use in multi-center studies by scanning five volunteers at three different sites. We determined the inter-site bias, inter-site and intra-site coefficient of variation (CoV) for typical morphometric measures [i.e., gray matter (GM) probability maps used in voxel-based morphometry] and the four quantitative parameters. The inter-site bias and CoV were smaller than 3.1 and 8%, respectively, except for the inter-site CoV of R2(*) (<20%). The GM probability maps based on the MT parameter maps had a 14% higher inter-site reproducibility than maps based on conventional T1-weighted images. The low inter-site bias and variance in the parameters and derived GM probability maps confirm the high comparability of the quantitative maps across sites and time points. The reliability, short acquisition time, high resolution and the detailed insights into the brain microstructure provided by MPM makes it an efficient tool for multi-center imaging studies.

Hydrogen and oxygen isotope behaviors during variable degrees of upper mantle melting: Example from the basaltic glasses from Macquarie Island

We present measurements of hydrogen and oxygen isotopes in MORB glasses from Macquarie Island (SW. Pacific Ocean) coupled with determination of bulk H2O content by two independent techniques: total dehydration and FTIR. The incompatible trace elements in these glasses vary by a factor of 12 to 17, with K2O varying from 0.1 to 1.7 wt.%; these ranges reflect a variable degree of closed-system mantle melting, estimated from 1 to 15%. Water concentrations determined by the two techniques match well, yielding a range from 0.25 to 1.49 wt.% which correlates positively with all of the measured incompatible trace elements, suggesting that water is un-degassed, and behaves conservatively during mantle melting. Also, the agreement between the FTIR-determined and extracted water contents gives us confidence that the measured isotopic values of hydrogen reflect that of the mantle. Comparison of the range of water content with that of other incompatible trace elements allows estimation of the water partition coefficient in lherzolite, 0.0208 (ranging from 0.017 to 0.023), and the water content in the source, 386 ppm (ranging from 370 to 440 ppm). We observe a fairly narrow range in delta D and delta O-18 values of -75.5 +/- 4.5 parts per thousand and 5.50 +/- 0 .05 parts per thousand respectively, that can be explained by partial melting of normal lherzolitic mantle. The measured delta D and delta O-18 values of Macquarie Island glasses that range from nepheline- to hypersthene-normative, and from MORB to EMORB in composition, are identical to those in average global MORB. The observed lack of variation of delta D and delta O-18 with 1 to 15% degree of mantle melting is consistent with a bulk melting model of delta D and delta O-18 fractionation, in which water is rapidly scavenged into the first partial melt. The narrow ranges of delta D and delta O-18 in normal mantle are mostly due to the buffering effect of clino- and orthopyroxenes in the residual assemblage; additionally, fast ``wet'' diffusion of oxygen and hydrogen isotopes through the melting regions may further smooth isotopic differences. (C) 2012 Elsevier B.V. All rights reserved.

ADC mapping of chronic cerebral hypoperfusion induced by carotid artery stenosis.

BACKGROUND: Carotid artery stenosis is associated with the occurrence of acute and chronic ischemic lesions that increase with age in the elderly population. Diffusion Imaging and ADC mapping may be an appropriate method to investigate patients with chronic hypoperfusion consecutive to carotid stenosis. This non-invasive technique allows to investigate brain integrity and structure, in particular hypoperfusion induced by carotid stenosis diseases. The aim of this study was to evaluate the impact of a carotid stenosis on the parenchyma using ADC mapping. METHODS: Fifty-nine patients with symptomatic (33) and asymptomatic (26) carotid stenosis were recruited from our multidisciplinary consultation. Both groups demonstrated a similar degree of stenosis. All patients underwent MRI of the brain including diffusion-weighted MR imaging with ADC mapping. Regions of interest were defined in the anterior and posterior paraventricular regions both ipsilateral and contralateral to the stenosis (anterior circulation). The same analysis was performed for the thalamic and occipital regions (posterior circulation). RESULTS: ADC values of the affected vascular territory were significantly higher on the side of the stenosis in the periventricular anterior (P<0.001) and posterior (P<0.01) area. There was no difference between ipsilateral and contralateral ADC values in the thalamic and occipital regions. CONCLUSIONS: We have shown that carotid stenosis is associated with significantly higher ADC values in the anterior circulation, probably reflecting an impact of chronic hypoperfusion on the brain parenchyma in symptomatic and asymptomatic patients. This is consistent with previous data in the literature.

Successful migration of three tracers without identification of sentinel nodes during intraoperative lymphatic mapping for non-small cell lung cancer.

Prospective comparative evaluation of patent V blue, fluorescein and (99m)TC-nanocolloids for intraoperative sentinel lymph node (SLN) mapping during surgery for non-small cell lung cancer (NSCLC). Ten patients with peripherally localised clinical stage I NSCLC underwent thoracotomy and peritumoral subpleural injection of 2 ml of patent V blue dye, 1 ml of 10% fluorescein and 1ml of (99m)Tc-nanocolloids (0.4 mCi). The migration and spatial distribution pattern of the tracers was assessed by direct visualisation (patent V blue), visualisation of fluorescence signalling by a lamp of Wood (fluorescein) and radioactivity counting with a hand held gamma-probe ((99m)Tc-nanocolloids). Lymph nodes at interlobar (ATS 11), hilar (ATS 10) and mediastinal (right ATS 2,4,7; left ATS 5,6,7) levels were systematically assessed every 10 min up to 60 min after injection, followed by lobectomy and formal lymph node dissection. Successful migration from the peritumoral area to the mediastinum was observed for all three tracers up to 60 min after injection. The interlobar lympho-fatty tissue (station ATS 11) revealed an early and preferential accumulation of all three tracers for all tumours assessed and irrespective of the tumour localisation. However, no preferential accumulation in one or two distinct lymph nodes was observed up to 60 min after injection for all three tracers assessed. Intraoperative SLN mapping revealed successful migration of the tracers from the site of peritumoral injection to the mediastinum, but in a diffuse pattern without preferential accumulation in sentinel lymph nodes.

Automatic Decision-Oriented Mapping of Pollution Data

The paper deals with the development and application of the methodology for automatic mapping of pollution/contamination data. General Regression Neural Network (GRNN) is considered in detail and is proposed as an efficient tool to solve this problem. The automatic tuning of isotropic and an anisotropic GRNN model using cross-validation procedure is presented. Results are compared with k-nearest-neighbours interpolation algorithm using independent validation data set. Quality of mapping is controlled by the analysis of raw data and the residuals using variography. Maps of probabilities of exceeding a given decision level and ?thick? isoline visualization of the uncertainties are presented as examples of decision-oriented mapping. Real case study is based on mapping of radioactively contaminated territories.