Learning wind fields with multiple kernels

This paper presents multiple kernel learning (MKL) regression as an exploratory spatial data analysis and modelling tool. The MKL approach is introduced as an extension of support vector regression, where MKL uses dedicated kernels to divide a given task into sub-problems and to treat them separately in an effective way. It provides better interpretability to non-linear robust kernel regression at the cost of a more complex numerical optimization. In particular, we investigate the use of MKL as a tool that allows us to avoid using ad-hoc topographic indices as covariables in statistical models in complex terrains. Instead, MKL learns these relationships from the data in a non-parametric fashion. A study on data simulated from real terrain features confirms the ability of MKL to enhance the interpretability of data-driven models and to aid feature selection without degrading predictive performances. Here we examine the stability of the MKL algorithm with respect to the number of training data samples and to the presence of noise. The results of a real case study are also presented, where MKL is able to exploit a large set of terrain features computed at multiple spatial scales, when predicting mean wind speed in an Alpine region.

Multiple Kernel Learning of Environmental Data. Case study: Analysis and Mapping of Wind Fields

The paper presents the Multiple Kernel Learning (MKL) approach as a modelling and data exploratory tool and applies it to the problem of wind speed mapping. Support Vector Regression (SVR) is used to predict spatial variations of the mean wind speed from terrain features (slopes, terrain curvature, directional derivatives) generated at different spatial scales. Multiple Kernel Learning is applied to learn kernels for individual features and thematic feature subsets, both in the context of feature selection and optimal parameters determination. An empirical study on real-life data confirms the usefulness of MKL as a tool that enhances the interpretability of data-driven models.

Kernel-based Mapping of Meteorological Fields in Complex Orography

Due to the advances in sensor networks and remote sensing technologies, the acquisition and storage rates of meteorological and climatological data increases every day and ask for novel and efficient processing algorithms. A fundamental problem of data analysis and modeling is the spatial prediction of meteorological variables in complex orography, which serves among others to extended climatological analyses, for the assimilation of data into numerical weather prediction models, for preparing inputs to hydrological models and for real time monitoring and short-term forecasting of weather.In this thesis, a new framework for spatial estimation is proposed by taking advantage of a class of algorithms emerging from the statistical learning theory. Nonparametric kernel-based methods for nonlinear data classification, regression and target detection, known as support vector machines (SVM), are adapted for mapping of meteorological variables in complex orography.With the advent of high resolution digital elevation models, the field of spatial prediction met new horizons. In fact, by exploiting image processing tools along with physical heuristics, an incredible number of terrain features which account for the topographic conditions at multiple spatial scales can be extracted. Such features are highly relevant for the mapping of meteorological variables because they control a considerable part of the spatial variability of meteorological fields in the complex Alpine orography. For instance, patterns of orographic rainfall, wind speed and cold air pools are known to be correlated with particular terrain forms, e.g. convex/concave surfaces and upwind sides of mountain slopes.Kernel-based methods are employed to learn the nonlinear statistical dependence which links the multidimensional space of geographical and topographic explanatory variables to the variable of interest, that is the wind speed as measured at the weather stations or the occurrence of orographic rainfall patterns as extracted from sequences of radar images. Compared to low dimensional models integrating only the geographical coordinates, the proposed framework opens a way to regionalize meteorological variables which are multidimensional in nature and rarely show spatial auto-correlation in the original space making the use of classical geostatistics tangled.The challenges which are explored during the thesis are manifolds. First, the complexity of models is optimized to impose appropriate smoothness properties and reduce the impact of noisy measurements. Secondly, a multiple kernel extension of SVM is considered to select the multiscale features which explain most of the spatial variability of wind speed. Then, SVM target detection methods are implemented to describe the orographic conditions which cause persistent and stationary rainfall patterns. Finally, the optimal splitting of the data is studied to estimate realistic performances and confidence intervals characterizing the uncertainty of predictions.The resulting maps of average wind speeds find applications within renewable resources assessment and opens a route to decrease the temporal scale of analysis to meet hydrological requirements. Furthermore, the maps depicting the susceptibility to orographic rainfall enhancement can be used to improve current radar-based quantitative precipitation estimation and forecasting systems and to generate stochastic ensembles of precipitation fields conditioned upon the orography.

Synthesis of highly focused fields with circular polarization at any transverse plane

We develop a method for generating focused vector beams with circular polarization at any transverse plane. Based on the Richards-Wolf vector model, we derive analytical expressions to describe the propagation of these set of beams near the focal area. Since the polarization and the amplitude of the input beam are not uniform, an interferometric system capable of generating spatially-variant polarized beams has to be used. In particular, this wavefront is manipulated by means of spatial light modulators displaying computer generated holograms and subsequently focused using a high numerical aperture objective lens. Experimental results using a NA=0.85 system are provided: irradiance and Stokes images of the focused field at different planes near the focal plane are presented and compared with those obtained by numerical simulation.

Dielectric Behavior of Natural Rubber Composites in Microwave Fields

In this article, we report the preparation of conducting natural rubber (NR) with polyaniline (Pani). NR was made into a conductive material by the compounding of NR with Pani in powder form. NR latex was made into a conductive material by the in situ polymerization of aniline in the presence of NR latex. Different compositions of Pani- NR semi-interpenetrating networks were prepared, and the dielectric properties of all of the samples were determined in microwave frequencies. The cavity perturbation techpique was used for this study. A HP8510 vector network analyzer with a rectangular cavity resonator was used for this study. S bands 2-4 GHz in frequency were used. Thermal studies were also carried out with thermogravimetric analysis and differential scanning calorimetry.

Dielectric Behavior of Natural Rubber Composites in Microwave Fields

In this article, we report the preparation of conducting natural rubber (NR) with polyaniline (Pani). NR was made into a conductive material by the compounding of NR with Pani in powder form. NR latex was made into a conductive material by the in situ polymerization of aniline in the presence of NR latex. Different compositions of Pani- NR semi-interpenetrating networks were prepared, and the dielectric properties of all of the samples were determined in microwave frequencies. The cavity perturbation techpique was used for this study. A HP8510 vector network analyzer with a rectangular cavity resonator was used for this study. S bands 2-4 GHz in frequency were used. Thermal studies were also carried out with thermogravimetric analysis and differential scanning calorimetry.

A Vector Signal Processing Approach to Color

Surface (Lambertain) color is a useful visual cue for analyzing material composition of scenes. This thesis adopts a signal processing approach to color vision. It represents color images as fields of 3D vectors, from which we extract region and boundary information. The first problem we face is one of secondary imaging effects that makes image color different from surface color. We demonstrate a simple but effective polarization based technique that corrects for these effects. We then propose a systematic approach of scalarizing color, that allows us to augment classical image processing tools and concepts for multi-dimensional color signals.

Comparing Support Vector Machines with Gaussian Kernels to Radial Basis Function Classifiers

The Support Vector (SV) machine is a novel type of learning machine, based on statistical learning theory, which contains polynomial classifiers, neural networks, and radial basis function (RBF) networks as special cases. In the RBF case, the SV algorithm automatically determines centers, weights and threshold such as to minimize an upper bound on the expected test error. The present study is devoted to an experimental comparison of these machines with a classical approach, where the centers are determined by $k$--means clustering and the weights are found using error backpropagation. We consider three machines, namely a classical RBF machine, an SV machine with Gaussian kernel, and a hybrid system with the centers determined by the SV method and the weights trained by error backpropagation. Our results show that on the US postal service database of handwritten digits, the SV machine achieves the highest test accuracy, followed by the hybrid approach. The SV approach is thus not only theoretically well--founded, but also superior in a practical application.

Vector-Based Integration of Local and Long-Range Information in Visual Cortex

Integration of inputs by cortical neurons provides the basis for the complex information processing performed in the cerebral cortex. Here, we propose a new analytic framework for understanding integration within cortical neuronal receptive fields. Based on the synaptic organization of cortex, we argue that neuronal integration is a systems--level process better studied in terms of local cortical circuitry than at the level of single neurons, and we present a method for constructing self-contained modules which capture (nonlinear) local circuit interactions. In this framework, receptive field elements naturally have dual (rather than the traditional unitary influence since they drive both excitatory and inhibitory cortical neurons. This vector-based analysis, in contrast to scalarsapproaches, greatly simplifies integration by permitting linear summation of inputs from both "classical" and "extraclassical" receptive field regions. We illustrate this by explaining two complex visual cortical phenomena, which are incompatible with scalar notions of neuronal integration.

Support Vector Machines: Training and Applications

The Support Vector Machine (SVM) is a new and very promising classification technique developed by Vapnik and his group at AT&T Bell Labs. This new learning algorithm can be seen as an alternative training technique for Polynomial, Radial Basis Function and Multi-Layer Perceptron classifiers. An interesting property of this approach is that it is an approximate implementation of the Structural Risk Minimization (SRM) induction principle. The derivation of Support Vector Machines, its relationship with SRM, and its geometrical insight, are discussed in this paper. Training a SVM is equivalent to solve a quadratic programming problem with linear and box constraints in a number of variables equal to the number of data points. When the number of data points exceeds few thousands the problem is very challenging, because the quadratic form is completely dense, so the memory needed to store the problem grows with the square of the number of data points. Therefore, training problems arising in some real applications with large data sets are impossible to load into memory, and cannot be solved using standard non-linear constrained optimization algorithms. We present a decomposition algorithm that can be used to train SVM's over large data sets. The main idea behind the decomposition is the iterative solution of sub-problems and the evaluation of, and also establish the stopping criteria for the algorithm. We present previous approaches, as well as results and important details of our implementation of the algorithm using a second-order variant of the Reduced Gradient Method as the solver of the sub-problems. As an application of SVM's, we present preliminary results we obtained applying SVM to the problem of detecting frontal human faces in real images.

Neurofuzzy network model construction using Bézier-Bernstein polynomial functions

Neurofuzzy modelling systems combine fuzzy logic with quantitative artificial neural networks via a concept of fuzzification by using a fuzzy membership function usually based on B-splines and algebraic operators for inference, etc. The paper introduces a neurofuzzy model construction algorithm using Bezier-Bernstein polynomial functions as basis functions. The new network maintains most of the properties of the B-spline expansion based neurofuzzy system, such as the non-negativity of the basis functions, and unity of support but with the additional advantages of structural parsimony and Delaunay input space partitioning, avoiding the inherent computational problems of lattice networks. This new modelling network is based on the idea that an input vector can be mapped into barycentric co-ordinates with respect to a set of predetermined knots as vertices of a polygon (a set of tiled Delaunay triangles) over the input space. The network is expressed as the Bezier-Bernstein polynomial function of barycentric co-ordinates of the input vector. An inverse de Casteljau procedure using backpropagation is developed to obtain the input vector's barycentric co-ordinates that form the basis functions. Extension of the Bezier-Bernstein neurofuzzy algorithm to n-dimensional inputs is discussed followed by numerical examples to demonstrate the effectiveness of this new data based modelling approach.

Alboserpin, a Factor Xa Inhibitor from the Mosquito Vector of Yellow Fever, Binds Heparin and Membrane Phospholipids and Exhibits Antithrombotic Activity

The molecular mechanism of factor Xa (FXa) inhibition by Alboserpin, the major salivary gland anticoagulant from the mosquito and yellow fever vector Aedes albopictus, has been characterized. cDNA of Alboserpin predicts a 45-kDa protein that belongs to the serpin family of protease inhibitors. Recombinant Alboserpin displays stoichiometric, competitive, reversible and tight binding to FXa (picomolar range). Binding is highly specific and is not detectable for FX, catalytic site-blocked FXa, thrombin, and 12 other enzymes. Alboserpin displays high affinity binding to heparin (K(D) similar to 20 nM), but no change in FXa inhibition was observed in the presence of the cofactor, implying that bridging mechanisms did not take place. Notably, Alboserpin was also found to interact with phosphatidylcholine and phosphatidylethanolamine but not with phosphatidylserine. Further, annexin V (in the absence of Ca(2+)) or heparin outcompetes Alboserpin for binding to phospholipid vesicles, suggesting a common binding site. Consistent with its activity, Alboserpin blocks prothrombinase activity and increases both prothrombin time and activated partial thromboplastin time in vitro or ex vivo. Furthermore, Alboserpin prevents thrombus formation provoked by ferric chloride injury of the carotid artery and increases bleeding in a dose-dependent manner. Alboserpin emerges as an atypical serpin that targets FXa and displays unique phospholipid specificity. It conceivably uses heparin and phosphatidylcholine/phosphatidylethanolamine as anchors to increase protein localization and effective concentration at sites of injury, cell activation, or inflammation.

Foliations and polynomial diffeomorphisms of R(3)

Let Y = (f, g, h): R(3) -> R(3) be a C(2) map and let Spec(Y) denote the set of eigenvalues of the derivative DY(p), when p varies in R(3). We begin proving that if, for some epsilon > 0, Spec(Y) boolean AND (-epsilon, epsilon) = empty set, then the foliation F(k), with k is an element of {f, g, h}, made up by the level surfaces {k = constant}, consists just of planes. As a consequence, we prove a bijectivity result related to the three-dimensional case of Jelonek`s Jacobian Conjecture for polynomial maps of R(n).

Reversible and irreversible magnetization components behavior in Ni nanowires

Polycrystalline Ni nanowires were electrodeposited in nanoporous anodized alumina membranes with mean diameter of approximately 42 nm. Their magnetic properties were studied at 300 K, by measurements of recoil curves from demagnetized state and also from saturated state. M(rev) and M(irr) components were obtained and M(rev)(M(irr)) H curves were constructed from the experimental data. These curves showed a behavior that suggests a non-uniform reversal mode influenced by the presence of dipolar interactions in the system. A qualitative approach to this behavior is obtained using a Stoner-Wohlfarth model modified by a mean field term and local interaction fields. (C) 2008 Elsevier B.V. All rights reserved.

A NOTE ON FREE GROUPS IN THE RING OF FRACTIONS OF SKEW POLYNOMIAL RINGS

Let L be a function field over the rationals and let D denote the skew field of fractions of L[t; sigma], the skew polynomial ring in t, over L, with automorphism sigma. We prove that the multiplicative group D(x) of D contains a free noncyclic subgroup.