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.

Properties of functional brain networks correlate with frequency of psychogenic non-epileptic seizures.

Abnormalities in the topology of brain networks may be an important feature and etiological factor for psychogenic non-epileptic seizures (PNES). To explore this possibility, we applied a graph theoretical approach to functional networks based on resting state EEGs from 13 PNES patients and 13 age- and gender-matched controls. The networks were extracted from Laplacian-transformed time-series by a cross-correlation method. PNES patients showed close to normal local and global connectivity and small-world structure, estimated with clustering coefficient, modularity, global efficiency, and small-worldness (SW) metrics, respectively. Yet the number of PNES attacks per month correlated with a weakness of local connectedness and a skewed balance between local and global connectedness quantified with SW, all in EEG alpha band. In beta band, patients demonstrated above-normal resiliency, measured with assortativity coefficient, which also correlated with the frequency of PNES attacks. This interictal EEG phenotype may help improve differentiation between PNES and epilepsy. The results also suggest that local connectivity could be a target for therapeutic interventions in PNES. Selective modulation (strengthening) of local connectivity might improve the skewed balance between local and global connectivity and so prevent PNES events.

Synchronous versus asynchronous modeling of gene regulatory networks.

MOTIVATION: In silico modeling of gene regulatory networks has gained some momentum recently due to increased interest in analyzing the dynamics of biological systems. This has been further facilitated by the increasing availability of experimental data on gene-gene, protein-protein and gene-protein interactions. The two dynamical properties that are often experimentally testable are perturbations and stable steady states. Although a lot of work has been done on the identification of steady states, not much work has been reported on in silico modeling of cellular differentiation processes. RESULTS: In this manuscript, we provide algorithms based on reduced ordered binary decision diagrams (ROBDDs) for Boolean modeling of gene regulatory networks. Algorithms for synchronous and asynchronous transition models have been proposed and their corresponding computational properties have been analyzed. These algorithms allow users to compute cyclic attractors of large networks that are currently not feasible using existing software. Hereby we provide a framework to analyze the effect of multiple gene perturbation protocols, and their effect on cell differentiation processes. These algorithms were validated on the T-helper model showing the correct steady state identification and Th1-Th2 cellular differentiation process. AVAILABILITY: The software binaries for Windows and Linux platforms can be downloaded from http://si2.epfl.ch/~garg/genysis.html.

Machine learning algorithms for spatial data. Case studies: Environmental pollution, natural hazards, renewable resources

This paper presents general problems and approaches for the spatial data analysis using machine learning algorithms. Machine learning is a very powerful approach to adaptive data analysis, modelling and visualisation. The key feature of the machine learning algorithms is that they learn from empirical data and can be used in cases when the modelled environmental phenomena are hidden, nonlinear, noisy and highly variable in space and in time. Most of the machines learning algorithms are universal and adaptive modelling tools developed to solve basic problems of learning from data: classification/pattern recognition, regression/mapping and probability density modelling. In the present report some of the widely used machine learning algorithms, namely artificial neural networks (ANN) of different architectures and Support Vector Machines (SVM), are adapted to the problems of the analysis and modelling of geo-spatial data. Machine learning algorithms have an important advantage over traditional models of spatial statistics when problems are considered in a high dimensional geo-feature spaces, when the dimension of space exceeds 5. Such features are usually generated, for example, from digital elevation models, remote sensing images, etc. An important extension of models concerns considering of real space constrains like geomorphology, networks, and other natural structures. Recent developments in semi-supervised learning can improve modelling of environmental phenomena taking into account on geo-manifolds. An important part of the study deals with the analysis of relevant variables and models' inputs. This problem is approached by using different feature selection/feature extraction nonlinear tools. To demonstrate the application of machine learning algorithms several interesting case studies are considered: digital soil mapping using SVM, automatic mapping of soil and water system pollution using ANN; natural hazards risk analysis (avalanches, landslides), assessments of renewable resources (wind fields) with SVM and ANN models, etc. The dimensionality of spaces considered varies from 2 to more than 30. Figures 1, 2, 3 demonstrate some results of the studies and their outputs. Finally, the results of environmental mapping are discussed and compared with traditional models of geostatistics.

The policy-making structure of European regulatory networks and the domestic adoption of standards

European regulatory networks (ERNs) constitute the main governance instrument for the informal co-ordination of public regulation at the European Union (EU) level. They are in charge of co-ordinating national regulators and ensuring the implementation of harmonized regulatory policies across the EU, while also offering sector-specific expertise to the Commission. To this aim, ERNs develop 'best practices' and benchmarking procedures in the form of standards, norms and guidelines to be adopted in member states. In this paper, we focus on the Committee of European Securities Regulators and examine the consequences of the policy-making structure of ERNs on the domestic adoption of standards. We find that the regulators of countries with larger financial industries tend to occupy more central positions in the network, especially among newer member states. In turn, network centrality is associated with a more prompt domestic adoption of standards.

Clustering and hot spot detection in socio-economic spatio-temporal data

Distribution of socio-economic features in urban space is an important source of information for land and transportation planning. The metropolization phenomenon has changed the distribution of types of professions in space and has given birth to different spatial patterns that the urban planner must know in order to plan a sustainable city. Such distributions can be discovered by statistical and learning algorithms through different methods. In this paper, an unsupervised classification method and a cluster detection method are discussed and applied to analyze the socio-economic structure of Switzerland. The unsupervised classification method, based on Ward's classification and self-organized maps, is used to classify the municipalities of the country and allows to reduce a highly-dimensional input information to interpret the socio-economic landscape. The cluster detection method, the spatial scan statistics, is used in a more specific manner in order to detect hot spots of certain types of service activities. The method is applied to the distribution services in the agglomeration of Lausanne. Results show the emergence of new centralities and can be analyzed in both transportation and social terms.

Comparison of early cortical networks in efficient and inefficient visual search: an event-related potential study.

Functional magnetic resonance imaging studies have indicated that efficient feature search (FS) and inefficient conjunction search (CS) activate partially distinct frontoparietal cortical networks. However, it remains a matter of debate whether the differences in these networks reflect differences in the early processing during FS and CS. In addition, the relationship between the differences in the networks and spatial shifts of attention also remains unknown. We examined these issues by applying a spatio-temporal analysis method to high-resolution visual event-related potentials (ERPs) and investigated how spatio-temporal activation patterns differ for FS and CS tasks. Within the first 450 msec after stimulus onset, scalp potential distributions (ERP maps) revealed 7 different electric field configurations for each search task. Configuration changes occurred simultaneously in the two tasks, suggesting that contributing processes were not significantly delayed in one task compared to the other. Despite this high spatial and temporal correlation, two ERP maps (120-190 and 250-300 msec) differed between the FS and CS. Lateralized distributions were observed only in the ERP map at 250-300 msec for the FS. This distribution corresponds to that previously described as the N2pc component (a negativity in the time range of the N2 complex over posterior electrodes of the hemisphere contralateral to the target hemifield), which has been associated with the focusing of attention onto potential target items in the search display. Thus, our results indicate that the cortical networks involved in feature and conjunction searching partially differ as early as 120 msec after stimulus onset and that the differences between the networks employed during the early stages of FS and CS are not necessarily caused by spatial attention shifts.

Error and attack tolerance of layered complex networks.

Many complex systems may be described by not one but a number of complex networks mapped on each other in a multi-layer structure. Because of the interactions and dependencies between these layers, the state of a single layer does not necessarily reflect well the state of the entire system. In this paper we study the robustness of five examples of two-layer complex systems: three real-life data sets in the fields of communication (the Internet), transportation (the European railway system), and biology (the human brain), and two models based on random graphs. In order to cover the whole range of features specific to these systems, we focus on two extreme policies of system's response to failures, no rerouting and full rerouting. Our main finding is that multi-layer systems are much more vulnerable to errors and intentional attacks than they appear from a single layer perspective.

Arbuscular mycorrhizal fungi: genetics of multigenomic, clonal networks and its ecological consequences

Arbuscular mycorrhizal fungi are thought to have remained asexual for 400 million years although recent studies have suggested that considerable genetic and phenotypic variation could potentially exist in populations. A brief discussion of these multigenomic organisms is presented. (C) 2003 The Linnean Society of London.

Validation of network communicability metrics for the analysis of brain structural networks.

Computational network analysis provides new methods to analyze the brain's structural organization based on diffusion imaging tractography data. Networks are characterized by global and local metrics that have recently given promising insights into diagnosis and the further understanding of psychiatric and neurologic disorders. Most of these metrics are based on the idea that information in a network flows along the shortest paths. In contrast to this notion, communicability is a broader measure of connectivity which assumes that information could flow along all possible paths between two nodes. In our work, the features of network metrics related to communicability were explored for the first time in the healthy structural brain network. In addition, the sensitivity of such metrics was analysed using simulated lesions to specific nodes and network connections. Results showed advantages of communicability over conventional metrics in detecting densely connected nodes as well as subsets of nodes vulnerable to lesions. In addition, communicability centrality was shown to be widely affected by the lesions and the changes were negatively correlated with the distance from lesion site. In summary, our analysis suggests that communicability metrics that may provide an insight into the integrative properties of the structural brain network and that these metrics may be useful for the analysis of brain networks in the presence of lesions. Nevertheless, the interpretation of communicability is not straightforward; hence these metrics should be used as a supplement to the more standard connectivity network metrics.

Activation and inhibition of bimanual movements in school-aged children

The development of motor activation and inhibition was compared in 6-to-12 year-olds. Children had to initiate or stop the externally paced movements of one hand, while maintaining that of the other hand. The time needed to perform the switching task (RT) and the spatio-temporal variables show different agerelated evolutions depending on the coordination pattern (inor anti-phase) and the type of transition (activation, selective inhibition, non selective inhibition) required. In the anti-phase mode, activation perturbs the younger subjects' responses while temporal and spatial stabilities transiently decrease around 9 years when activating in the in-phase mode. Aged-related changes differed between inhibition and activation in the antiphase mode, suggesting either the involvement of distinct neural networks or the existence of a single network that is reorganized. In contrast, stopping or adding one hand in the in-phase mode shows similar aged-related improvement. We suggest that selectively stopping or activating one arm during symmetrical coordination rely on the two faces of a common processing in which activation could be the release of inhibition

Stochastic models and numerical algorithms for a class of regulatory gene networks.

Regulatory gene networks contain generic modules, like those involving feedback loops, which are essential for the regulation of many biological functions (Guido et al. in Nature 439:856-860, 2006). We consider a class of self-regulated genes which are the building blocks of many regulatory gene networks, and study the steady-state distribution of the associated Gillespie algorithm by providing efficient numerical algorithms. We also study a regulatory gene network of interest in gene therapy, using mean-field models with time delays. Convergence of the related time-nonhomogeneous Markov chain is established for a class of linear catalytic networks with feedback loops.

Atmospheric deposition and migration of artificial radionuclides in Alpine soils (Val Piora, Switzerland) compared to the distribution of selected major and trace elements.

Artificial radionuclides ((137)Cs, (90)Sr, Pu, and (241)Am) are present in soils because of Nuclear Weapon Tests and accidents in nuclear facilities. Their distribution in soil depth varies according to soil characteristics, their own chemical properties, and their deposition history. For this project, we studied the atmospheric deposition of (137)Cs, (90)Sr, Pu, (241)Am, (210)Pb, and stable Pb. We compared the distribution of these elements in soil profiles from different soil types from an alpine Valley (Val Piora, Switzerland) with the distribution of selected major and trace elements in the same soils. Our goals were to explain the distribution of the radioisotopes as a function of soil parameters and to identify stable elements with analogous behaviors. We found that Pu and (241)Am are relatively immobile and accumulate in the topsoil. In all soils, (90)Sr is more mobile and shows some accumulations at depth into Fe-Al rich horizons. This behavior is also observed for Cu and Zn, indicating that these elements may be used as chemical analogues for the migration of (90)Sr into the soil.