Fronts from complex two-dimensional dispersal kernels: theory and application to Reid's paradox

Bimodal dispersal probability distributions with characteristic distances differing by several orders of magnitude have been derived and favorably compared to observations by Nathan [Nature (London) 418, 409 (2002)]. For such bimodal kernels, we show that two-dimensional molecular dynamics computer simulations are unable to yield accurate front speeds. Analytically, the usual continuous-space random walks (CSRWs) are applied to two dimensions. We also introduce discrete-space random walks and use them to check the CSRW results (because of the inefficiency of the numerical simulations). The physical results reported are shown to predict front speeds high enough to possibly explain Reid's paradox of rapid tree migration. We also show that, for a time-ordered evolution equation, fronts are always slower in two dimensions than in one dimension and that this difference is important both for unimodal and for bimodal kernels

Anisotropic dispersion, space competition, and the slowdown of the Neolithic transition

The front speed of the Neolithic (farmer) spread in Europe decreased as it reached Northern latitudes, where the Mesolithic (huntergatherer) population density was higher. Here, we describe a reaction diffusion model with (i) an anisotropic dispersion kernel depending on the Mesolithic population density gradient and (ii) a modified population growth equation. Both effects are related to the space available for the Neolithic population. The model is able to explain the slowdown of the Neolithic front as observed from archaeological data

Spherical nonparametric estimators applied to the UGAMP model integration for AMIP

The aim of this paper is essentially twofold: first, to describe the use of spherical nonparametric estimators for determining statistical diagnostic fields from ensembles of feature tracks on a global domain, and second, to report the application of these techniques to data derived from a modern general circulation model. New spherical kernel functions are introduced that are more efficiently computed than the traditional exponential kernels. The data-driven techniques of cross-validation to determine the amount elf smoothing objectively, and adaptive smoothing to vary the smoothing locally, are also considered. Also introduced are techniques for combining seasonal statistical distributions to produce longer-term statistical distributions. Although all calculations are performed globally, only the results for the Northern Hemisphere winter (December, January, February) and Southern Hemisphere winter (June, July, August) cyclonic activity are presented, discussed, and compared with previous studies. Overall, results for the two hemispheric winters are in good agreement with previous studies, both for model-based studies and observational studies.

Inverse problems in dynamic cognitive modeling

Inverse problems for dynamical system models of cognitive processes comprise the determination of synaptic weight matrices or kernel functions for neural networks or neural/dynamic field models, respectively. We introduce dynamic cognitive modeling as a three tier top-down approach where cognitive processes are first described as algorithms that operate on complex symbolic data structures. Second, symbolic expressions and operations are represented by states and transformations in abstract vector spaces. Third, prescribed trajectories through representation space are implemented in neurodynamical systems. We discuss the Amari equation for a neural/dynamic field theory as a special case and show that the kernel construction problem is particularly ill-posed. We suggest a Tikhonov-Hebbian learning method as regularization technique and demonstrate its validity and robustness for basic examples of cognitive computations.

Road Sign Recognition based onInvariant Features using SupportVector Machine

Since last two decades researches have been working on developing systems that can assistsdrivers in the best way possible and make driving safe. Computer vision has played a crucialpart in design of these systems. With the introduction of vision techniques variousautonomous and robust real-time traffic automation systems have been designed such asTraffic monitoring, Traffic related parameter estimation and intelligent vehicles. Among theseautomatic detection and recognition of road signs has became an interesting research topic.The system can assist drivers about signs they don’t recognize before passing them.Aim of this research project is to present an Intelligent Road Sign Recognition System basedon state-of-the-art technique, the Support Vector Machine. The project is an extension to thework done at ITS research Platform at Dalarna University [25]. Focus of this research work ison the recognition of road signs under analysis. When classifying an image its location, sizeand orientation in the image plane are its irrelevant features and one way to get rid of thisambiguity is to extract those features which are invariant under the above mentionedtransformation. These invariant features are then used in Support Vector Machine forclassification. Support Vector Machine is a supervised learning machine that solves problemin higher dimension with the help of Kernel functions and is best know for classificationproblems.

An environment for knowledge discovery in biology

This paper describes a data mining environment for knowledge discovery in bioinformatics applications. The system has a generic kernel that implements the mining functions to be applied to input primary databases, with a warehouse architecture, of biomedical information. Both supervised and unsupervised classification can be implemented within the kernel and applied to data extracted from the primary database, with the results being suitably stored in a complex object database for knowledge discovery. The kernel also includes a specific high-performance library that allows designing and applying the mining functions in parallel machines. The experimental results obtained by the application of the kernel functions are reported. © 2003 Elsevier Ltd. All rights reserved.

Multivariate sobolev-type orthogonal polynomials

Multivariate orthogonal polynomials associated with a Sobolev-type inner product, that is, an inner product defined by adding to a measure the evaluation of the gradients in a fixed point, are studied. Orthogonal polynomials and kernel functions associated with this new inner product can be explicitly expressed in terms of those corresponding with the original measure. We apply our results to the particular case of the classical orthogonal polynomials on the unit ball, and we obtain the asymptotics of the kernel functions. © 2011 Universidad de Jaén.

Learning kernels for support vector machines with polynomial powers of sigmoid

In the pattern recognition research field, Support Vector Machines (SVM) have been an effectiveness tool for classification purposes, being successively employed in many applications. The SVM input data is transformed into a high dimensional space using some kernel functions where linear separation is more likely. However, there are some computational drawbacks associated to SVM. One of them is the computational burden required to find out the more adequate parameters for the kernel mapping considering each non-linearly separable input data space, which reflects the performance of SVM. This paper introduces the Polynomial Powers of Sigmoid for SVM kernel mapping, and it shows their advantages over well-known kernel functions using real and synthetic datasets.

Learning with Kernels on Graphs: DAG-based kernels, data streams and RNA function prediction.

In many application domains data can be naturally represented as graphs. When the application of analytical solutions for a given problem is unfeasible, machine learning techniques could be a viable way to solve the problem. Classical machine learning techniques are defined for data represented in a vectorial form. Recently some of them have been extended to deal directly with structured data. Among those techniques, kernel methods have shown promising results both from the computational complexity and the predictive performance point of view. Kernel methods allow to avoid an explicit mapping in a vectorial form relying on kernel functions, which informally are functions calculating a similarity measure between two entities. However, the definition of good kernels for graphs is a challenging problem because of the difficulty to find a good tradeoff between computational complexity and expressiveness. Another problem we face is learning on data streams, where a potentially unbounded sequence of data is generated by some sources. There are three main contributions in this thesis. The first contribution is the definition of a new family of kernels for graphs based on Directed Acyclic Graphs (DAGs). We analyzed two kernels from this family, achieving state-of-the-art results from both the computational and the classification point of view on real-world datasets. The second contribution consists in making the application of learning algorithms for streams of graphs feasible. Moreover,we defined a principled way for the memory management. The third contribution is the application of machine learning techniques for structured data to non-coding RNA function prediction. In this setting, the secondary structure is thought to carry relevant information. However, existing methods considering the secondary structure have prohibitively high computational complexity. We propose to apply kernel methods on this domain, obtaining state-of-the-art results.

Linear latent force models using Gaussian Processes

Purely data-driven approaches for machine learning present difficulties when data are scarce relative to the complexity of the model or when the model is forced to extrapolate. On the other hand, purely mechanistic approaches need to identify and specify all the interactions in the problem at hand (which may not be feasible) and still leave the issue of how to parameterize the system. In this paper, we present a hybrid approach using Gaussian processes and differential equations to combine data-driven modeling with a physical model of the system. We show how different, physically inspired, kernel functions can be developed through sensible, simple, mechanistic assumptions about the underlying system. The versatility of our approach is illustrated with three case studies from motion capture, computational biology, and geostatistics.

Change of extreme rainfall indexes at Ebro River Basin

The purpose of this work is to provide a description of the heavy rainfall phenomenon on statistical tools from a Spanish region. We want to quantify the effect of the climate change to verify the rapidity of its evolution across the variation of the probability distributions. Our conclusions have special interest for the agrarian insurances, which may make estimates of costs more realistically. In this work, the analysis mainly focuses on: The distribution of consecutive days without rain for each gauge stations and season. We estimate density Kernel functions and Generalized Pareto Distribution (GPD) for a network of station from the Ebro River basin until a threshold value u. We can establish a relation between distributional parameters and regional characteristics. Moreover we analyze especially the tail of the probability distribution. These tails are governed by law of power means that the number of events n can be expressed as the power of another quantity x : n(x) = x? . ? can be estimated as the slope of log-log plot the number of events and the size. The most convenient way to analyze n(x) is using the empirical probability distribution. Pr(X mayor que x) ? x-?. The distribution of rainfall over percentile of order 0.95 from wet days at the seasonal scale and in a yearly scale with the same treatment of tails than in the previous section.

Patrones y procesos espaciales en poblaciones y comunidades vegetales: nuevas herramientas e hipótesis

Generalmente los patrones espaciales de puntos en ecología, se definen en el espacio bi-dimensional, donde cada punto representado por el par ordenado (x,y), resume la ubicación espacial de una planta. La importancia de los patrones espaciales de plantas radica en que proceden como respuesta ante importantes procesos ecológicos asociados a la estructura de una población o comunidad. Tales procesos incluyen fenómenos como la dispersión de semillas, la competencia por recursos, la facilitación, respuesta de las plantas ante algún tipo de estrés, entre otros. En esta tesis se evalúan los factores y potenciales procesos subyacentes, que explican los patrones de distribución espacial de la biodiversidad vegetal en diferentes ecosistemas como bosque mediterráneo, bosque tropical y matorral seco tropical; haciendo uso de nuevas metodologías para comprobar hipótesis relacionadas a los procesos espaciales. En este trabajo se utilizaron dos niveles ecológicos para analizar los procesos espaciales, el nivel de población y el nivel de comunidad, con el fin de evaluar la importancia relativa de las interacciones intraespecíficas e interespecíficas. Me centré en el uso de funciones estadísticas que resumen los patrones de puntos para explorar y hacer inferencias a partir de datos espaciales, empezando con la construcción de un nuevo modelo nulo para inferir variantes del síndrome de dispersión de una planta parásita en España central. Se analizó la dependencia de los patrones espaciales tanto de los hospedantes afectados como de los no-afectados y se observó fuerte dependencia a pequeña y mediana distancia. Se utilizaron dos funciones (kernel) para simular la dispersión de la especie parásita y se identificó consistencia de estos modelos con otros síndromes de dispersión adicionalmente a la autodispersión. Un segundo tema consistió en desarrollar un método ANOVA de dos vías? para patrones de puntos replicados donde el interés se concentró en evaluar la interacción de dos factores. Este método se aplicó a un caso de estudio que consitió en analizar la influencia de la topografía y la altitud sobre el patrón espacial de un arbusto dominante en matorral seco al sur del Ecuador, cuyos datos provienen de patrones de puntos replicados basados en diseño. Partiendo de una metodología desarrollada para procesos uni-factoriales, se construyó el método para procesos bi-factoriales y así poder evaluar el efecto de interacción. Se observó que la topografía por sí sola así como la interacción con la altitud presentaron efecto significativo sobre la formación del patrón espacial. Un tercer tema fue identificar la relación entre el patrón espacial y el síndrome de dispersión de la comunidad vegetal en el bosque tropical de la Isla de Barro Colorado (BCI), Panamá. Muchos estudios se han desarrollado en este bosque tropical y algunos han analizado la relación síndrome-patrón espacial, sin embargo lo novedoso de nuestro estudio es que se evaluaron un conjunto amplio de modelos (114 modelos) basados en procesos que incorporan la limitación de la dispersión y la heterogeneidad ambiental, y evalúan el efecto único y el efecto conjunto, para posteriormente seleccionar el modelo de mejor ajuste para cada especie. Más de la mitad de las especies presentaron patrón espacial consistente con el efecto conjutno de la limitación de la dispersión y heterogeneidad ambiental y el porcentaje restante de especies reveló en forma equitativa el efecto único de la heterogeneidad ambiental y efecto único de limitación de la dispersión. Finalmente, con la misma información del bosque tropical de BCI, y para entender las relaciones que subyacen para mantener el equilibrio de la biodiversidad, se desarrolló un índice de dispersión funcional local a nivel de individuo, que permita relacionar el patrón espacial con cuatro rasgos funcionales clave de las especies. Pese a que muchos estudios realizados involucran esta comunidad con la teoría neutral, se encontró que el ensamble de la comunidad de BCI está afectado por limitaciones de similaridad y de hábitat a diferentes escalas. ABSTRACT Overall the spatial point patterns in ecology are defined in two-dimensional space, where each point denoted by the (x,y) ordered pair, summarizes the spatial location of a plant. The spatial point patterns are essential because they arise in response to important ecological processes, associated with the structure of a population or community. Such processes include phenomena as seed dispersal, competition for resources, facilitation, and plant response to some type of stress, among others. In this thesis, some factors and potential underlying processes were evaluated in order to explain the spatial distribution patterns of plant biodiversity. It was done in different ecosystems such as Mediterranean forest, tropical forest and dry scrubland. For this purpose new methodologies were used to test hypothesis related to spatial processes. Two ecological levels were used to analyze the spatial processes, at population and community levels, in order to assess the relative importance of intraspecific and interspecific interactions. I focused on the use of spatial statistical functions to summarize point patterns to explore and make inferences from spatial data, starting with the construction of a new null model to infer variations about the dispersal syndrome of a parasitic plant in central Spain. Spatial dependence between point patterns in a multivariate point process of affected and unaffected hosts were analyzed and strong dependence was observed at small and medium distance. Two kernel functions were used to simulate the dispersion of parasitic plant and consistency of these models with other syndromes was identified, in addition to ballistic dispersion. A second issue was to analyze altitude and topography effects on the spatial population structure of a dominant shrub in the dry ecosystem in southern Ecuador, whose data come from replicated point patterns design-based. Based on a methodology developed for uni-factorial process, a method for bi-factorial processes was built to assess the interaction effect. The topography alone and interacting with altitude showed significant effect on the spatial pattern of shrub. A third issue was to identify the relationship between the spatial pattern and dispersal syndromes of plant community in the tropical forest of Barro Colorado Island (BCI), Panamá. Several studies have been developed in this tropical forest and some focused on the spatial pattern-syndrome relationship; however the novelty of our study is that a large set of models (114 models) including dispersal limitation and environmental heterogeneity were evaluated, used to identify the only and joint effect to subsequently select the best fit model for each species. Slightly more than fifty percent of the species showed spatial pattern consistent with only the dispersal limitation, and the remaining percentage of species revealed the only effect of environmental heterogeneity and habitat-dispersal limitation joined effect, equitably. Finally, with the same information from the tropical forest of BCI, and to understand the relationships underlying for balance of biodiversity, an index of the local functional dispersion was developed at the individual level, to relate the spatial pattern with four key functional traits of species. Although many studies involve this community with neutral theory, the assembly of the community is affected by similarity and habitat limitations at different scales.

Neural network-based wind vector retrieval from satellite scatterometer data

Obtaining wind vectors over the ocean is important for weather forecasting and ocean modelling. Several satellite systems used operationally by meteorological agencies utilise scatterometers to infer wind vectors over the oceans. In this paper we present the results of using novel neural network based techniques to estimate wind vectors from such data. The problem is partitioned into estimating wind speed and wind direction. Wind speed is modelled using a multi-layer perceptron (MLP) and a sum of squares error function. Wind direction is a periodic variable and a multi-valued function for a given set of inputs; a conventional MLP fails at this task, and so we model the full periodic probability density of direction conditioned on the satellite derived inputs using a Mixture Density Network (MDN) with periodic kernel functions. A committee of the resulting MDNs is shown to improve the results.

Neural network-based wind vector retrieval from satellite scatterometer data

Obtaining wind vectors over the ocean is important for weather forecasting and ocean modelling. Several satellite systems used operationally by meteorological agencies utilise scatterometers to infer wind vectors over the oceans. In this paper we present the results of using novel neural network based techniques to estimate wind vectors from such data. The problem is partitioned into estimating wind speed and wind direction. Wind speed is modelled using a multi-layer perceptron (MLP) and a sum of squares error function. Wind direction is a periodic variable and a multi-valued function for a given set of inputs; a conventional MLP fails at this task, and so we model the full periodic probability density of direction conditioned on the satellite derived inputs using a Mixture Density Network (MDN) with periodic kernel functions. A committee of the resulting MDNs is shown to improve the results.

Fractional Calculus of P-transforms

MSC 2010: 44A20, 33C60, 44A10, 26A33, 33C20, 85A99