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.

Linear random knots and their scaling behavior

We present here a nonbiased probabilistic method that allows us to consistently analyze knottedness of linear random walks with up to several hundred noncorrelated steps. The method consists of analyzing the spectrum of knots formed by multiple closures of the same open walk through random points on a sphere enclosing the walk. Knottedness of individual "frozen" configurations of linear chains is therefore defined by a characteristic spectrum of realizable knots. We show that in the great majority of cases this method clearly defines the dominant knot type of a walk, i.e., the strongest component of the spectrum. In such cases, direct end-to-end closure creates a knot that usually coincides with the knot type that dominates the random closure spectrum. Interestingly, in a very small proportion of linear random walks, the knot type is not clearly defined. Such walks can be considered as residing in a border zone of the configuration space of two or more knot types. We also characterize the scaling behavior of linear random knots.

Fast Geodesic Active Fields for Image Registration Based on Splitting and Augmented Lagrangian Approaches.

In this paper, we present an efficient numerical scheme for the recently introduced geodesic active fields (GAF) framework for geometric image registration. This framework considers the registration task as a weighted minimal surface problem. Hence, the data-term and the regularization-term are combined through multiplication in a single, parametrization invariant and geometric cost functional. The multiplicative coupling provides an intrinsic, spatially varying and data-dependent tuning of the regularization strength, and the parametrization invariance allows working with images of nonflat geometry, generally defined on any smoothly parametrizable manifold. The resulting energy-minimizing flow, however, has poor numerical properties. Here, we provide an efficient numerical scheme that uses a splitting approach; data and regularity terms are optimized over two distinct deformation fields that are constrained to be equal via an augmented Lagrangian approach. Our approach is more flexible than standard Gaussian regularization, since one can interpolate freely between isotropic Gaussian and anisotropic TV-like smoothing. In this paper, we compare the geodesic active fields method with the popular Demons method and three more recent state-of-the-art algorithms: NL-optical flow, MRF image registration, and landmark-enhanced large displacement optical flow. Thus, we can show the advantages of the proposed FastGAF method. It compares favorably against Demons, both in terms of registration speed and quality. Over the range of example applications, it also consistently produces results not far from more dedicated state-of-the-art methods, illustrating the flexibility of the proposed framework.

Evaluating effects of spectral training data distribution on continuous field mapping performance

Continuous field mapping has to address two conflicting remote sensing requirements when collecting training data. On one hand, continuous field mapping trains fractional land cover and thus favours mixed training pixels. On the other hand, the spectral signature has to be preferably distinct and thus favours pure training pixels. The aim of this study was to evaluate the sensitivity of training data distribution along fractional and spectral gradients on the resulting mapping performance. We derived four continuous fields (tree, shrubherb, bare, water) from aerial photographs as response variables and processed corresponding spectral signatures from multitemporal Landsat 5 TM data as explanatory variables. Subsequent controlled experiments along fractional cover gradients were then based on generalised linear models. Resulting fractional and spectral distribution differed between single continuous fields, but could be satisfactorily trained and mapped. Pixels with fractional or without respective cover were much more critical than pure full cover pixels. Error distribution of continuous field models was non-uniform with respect to horizontal and vertical spatial distribution of target fields. We conclude that a sampling for continuous field training data should be based on extent and densities in the fractional and spectral, rather than the real spatial space. Consequently, adequate training plots are most probably not systematically distributed in the real spatial space, but cover the gradient and covariate structure of the fractional and spectral space well. (C) 2009 International Society for Photogrammetry and Remote Sensing, Inc. (ISPRS). Published by Elsevier B.V. All rights reserved.

Igneous layering, fractional crystallization and growth of granitic plutons: The Dolbel batholith in SW Niger

This study reassesses the development of compositional layering during the growth of granitic plutons, with emphasis on fractional crystallization and its interaction with both injection and inflation-related deformation. The Dolbel batholith (SW Niger) consists of 14, kilometre-sized plutons emplaced by pulsed magma inputs. Each pluton has a coarse-grained core and a peripheral layered series. Rocks consist of albite (An(<= 11)), K-feldspar (Or(96 99), Ab(1) (4)), quartz, edenite (X(Mg)=0337-0.55), augite (X(Mg)=0.65-0.72) and accessories (apatite, titanite and Fe-Ti-oxides). Whole-rock compositions are metaluminous, sodic (K(2)O/Na(2)O=0.49-0.62) and iron-rich [FeO(tot)/(FeO(tot)+MgO)=0.65-0.82]. The layering is present as size-graded and modally graded, sub-vertical, rhythmic units. Each unit is composed of three layers, which are, towards the interior: edenite +/- plagioclase (C(a/p)), edenite+plagioclase+augite+quartz (C(q)), and edenite+plagioclase+augite+quartz+K-feldspar (C(k)). All phases except quartz show zoned microstructures consisting of external intercumulus overgrowths, a central section showing oscillatory zoning and, in the case of amphibole and titanite, complexly zoned cores. Ba and Sr contents of feldspars decrease towards the rims. Plagioclase crystal size distributions are similar in all units, suggesting that each unit experienced a similar thermal history. Edenite, characteristic of the basal C(a/p) layer, is the earliest phase to crystallize. Microtextures and phase diagrams suggest that edenite cores may have been brought up with magma batches at the site of emplacement and mechanically segregated along the crystallized wall, whereas outer zones of the same crystals formed in situ. The subsequent C(q) layers correspond to cotectic compositions in the Qz-Ab-Or phase diagram at P(H2O)=5 kbar. Each rhythmic unit may therefore correspond to a magma batch and their repetition to crystallization of recurrent magma recharges. Microtextures and chemical variations in major phases allow four main crystallization stages to be distinguished: (1) open-system crystallization in a stirred magma during magma emplacement, involving dissolution and overgrowth (core of edenite and titanite crystals); (2) in situ fractional crystallization in boundary layers (C(a/p) and C(q) layers); (3) equilibrium `en masse' eutectic crystallization (C(k) layers); (4) compaction and crystallization of the interstitial liquid in a highly crystallized mush (e. g. feldspar intercumulus overgrowths). It is concluded that the formation of the layered series in the Dolbel plutons corresponds principally to in situ differentiation of successive magma batches. The variable thickness of the Ck layers and the microtextures show that crystallization of a rhythmic unit stops and it is compacted when a new magma batch is injected into the chamber. Therefore, assembly of pulsed magma injections and fractional crystallization are independent, but complementary, processes during pluton construction.

The co-evolution of culturally inherited altruistic helping and cultural transmission under random group formation.

Limited migration results in kin selective pressure on helping behaviors under a wide range of ecological, demographic and life-history situations. However, such genetically determined altruistic helping can evolve only when migration is not too strong and group size is not too large. Cultural inheritance of helping behaviors may allow altruistic helping to evolve in groups of larger size because cultural transmission has the potential to markedly decrease the variance within groups and augment the variance between groups. Here, we study the co-evolution of culturally inherited altruistic helping behaviors and two alternative cultural transmission rules for such behaviors. We find that conformist transmission, where individuals within groups tend to copy prevalent cultural variants (e.g., beliefs or values), has a strong adverse effect on the evolution of culturally inherited helping traits. This finding is at variance with the commonly held view that conformist transmission is a crucial factor favoring the evolution of altruistic helping in humans. By contrast, we find that under one-to-many transmission, where individuals within groups tend to copy a "leader" (or teacher), altruistic helping can evolve in groups of any size, although the cultural transmission rule itself hitchhikes rather weakly with a selected helping trait. Our results suggest that culturally determined helping behaviors are more likely to be driven by "leaders" than by popularity, but the emergence and stability of the cultural transmission rules themselves should be driven by some extrinsic factors.