Three-dimensional inverse modelling of magnetic anomaly sources based on a genetic algorithm.

We present a modelling method to estimate the 3-D geometry and location of homogeneously magnetized sources from magnetic anomaly data. As input information, the procedure needs the parameters defining the magnetization vector (intensity, inclination and declination) and the Earth's magnetic field direction. When these two vectors are expected to be different in direction, we propose to estimate the magnetization direction from the magnetic map. Then, using this information, we apply an inversion approach based on a genetic algorithm which finds the geometry of the sources by seeking the optimum solution from an initial population of models in successive iterations through an evolutionary process. The evolution consists of three genetic operators (selection, crossover and mutation), which act on each generation, and a smoothing operator, which looks for the best fit to the observed data and a solution consisting of plausible compact sources. The method allows the use of non-gridded, non-planar and inaccurate anomaly data and non-regular subsurface partitions. In addition, neither constraints for the depth to the top of the sources nor an initial model are necessary, although previous models can be incorporated into the process. We show the results of a test using two complex synthetic anomalies to demonstrate the efficiency of our inversion method. The application to real data is illustrated with aeromagnetic data of the volcanic island of Gran Canaria (Canary Islands).

A continuous model for quasinilpotent operators.

A classical result due to Foias and Pearcy establishes a discrete model for every quasinilpotent operator acting on a separable, infinite-dimensional complex Hilbert space HH . More precisely, given a quasinilpotent operator T on HH , there exists a compact quasinilpotent operator K in HH such that T is similar to a part of K⊕K⊕⋯⊕K⊕⋯K⊕K⊕⋯⊕K⊕⋯ acting on the direct sum of countably many copies of HH . We show that a continuous model for any quasinilpotent operator can be provided. The consequences of such a model will be discussed in the context of C0C0 -semigroups of quasinilpotent operators.

Grouping genetic operators for the delineation of functional areas based on spatial interaction

The delineation of functional economic areas, or market areas, is a problem of high practical relevance, since the delineation of functional sets such as economic areas in the US, Travel-to-Work Areas in the United Kingdom, and their counterparts in other OECD countries are the basis of many statistical operations and policy making decisions at local level. This is a combinatorial optimisation problem defined as the partition of a given set of indivisible spatial units (covering a territory) into regions characterised by being (a) self-contained and (b) cohesive, in terms of spatial interaction data (flows, relationships). Usually, each region must reach a minimum size and self-containment level, and must be continuous. Although these optimisation problems have been typically solved through greedy methods, a recent strand of the literature in this field has been concerned with the use of evolutionary algorithms with ad hoc operators. Although these algorithms have proved to be successful in improving the results of some of the more widely applied official procedures, they are so time consuming that cannot be applied directly to solve real-world problems. In this paper we propose a new set of group-based mutation operators, featuring general operations over disjoint groups, tailored to ensure that all the constraints are respected during the operation to improve efficiency. A comparative analysis of our results with those from previous approaches shows that the proposed algorithm systematically improves them in terms of both quality and processing time, something of crucial relevance since it allows dealing with most large, real-world problems in reasonable time.

Lipschitz compact operators

We introduce the notion of Lipschitz compact (weakly compact, finite-rank, approximable) operators from a pointed metric space X into a Banach space E. We prove that every strongly Lipschitz p-nuclear operator is Lipschitz compact and every strongly Lipschitz p-integral operator is Lipschitz weakly compact. A theory of Lipschitz compact (weakly compact, finite-rank) operators which closely parallels the theory for linear operators is developed. In terms of the Lipschitz transpose map of a Lipschitz operator, we state Lipschitz versions of Schauder type theorems on the (weak) compactness of the adjoint of a (weakly) compact linear operator.

Trajectory-Based Morphological Operators: A Model for Efficient Image Processing

Mathematical morphology has been an area of intensive research over the last few years. Although many remarkable advances have been achieved throughout these years, there is still a great interest in accelerating morphological operations in order for them to be implemented in real-time systems. In this work, we present a new model for computing mathematical morphology operations, the so-called morphological trajectory model (MTM), in which a morphological filter will be divided into a sequence of basic operations. Then, a trajectory-based morphological operation (such as dilation, and erosion) is defined as the set of points resulting from the ordered application of the instant basic operations. The MTM approach allows working with different structuring elements, such as disks, and from the experiments, it can be extracted that our method is independent of the structuring element size and can be easily applied to industrial systems and high-resolution images.

Weighted composition operators on the predual and dual Banach spaces of Beurling algebras on Z

Let vv be a weight sequence on ZZ and let ψ,φψ,φ be complex-valued functions on ZZ such that φ(Z)⊂Zφ(Z)⊂Z. In this paper we study the boundedness, compactness and weak compactness of weighted composition operators Cψ,φCψ,φ on predual Banach spaces c0(Z,1/v)c0(Z,1/v) and dual Banach spaces ℓ∞(Z,1/v)ℓ∞(Z,1/v) of Beurling algebras ℓ1(Z,v)ℓ1(Z,v).

Inclusive education in Spain: how do skills, resources, and supports affect regular education teachers’ perceptions of inclusion?

This study examined regular education teachers’ perceptions of inclusion in elementary and secondary schools in Spain and how these perceptions may differ depending on teaching experience, skills, and the availability of resources and supports. Stratified random sampling procedures were used to draw a representative sample of 336 general education teachers (68 kindergarten, 133 elementary, and 135 secondary teachers) from the province of Alicante. The results indicated the acceptance of the principles of inclusion, although teacher skills, time, material resources, and personal supports for inclusion were deemed insufficient. Kindergarten and elementary teachers showed more positive perceptions of inclusion than secondary education teachers, and so did teachers with more personal supports and material resources than those with less supports and resources. The results are discussed in terms of its implications for practice in order to promote more inclusive classrooms in Spain.

FFT Interpolation From Nonuniform Samples Lying in a Regular Grid

This paper presents a method to interpolate a periodic band-limited signal from its samples lying at nonuniform positions in a regular grid, which is based on the FFT and has the same complexity order as this last algorithm. This kind of interpolation is usually termed “the missing samples problem” in the literature, and there exists a wide variety of iterative and direct methods for its solution. The one presented in this paper is a direct method that exploits the properties of the so-called erasure polynomial and provides a significant improvement on the most efficient method in the literature, which seems to be the burst error recovery (BER) technique of Marvasti’s The paper includes numerical assessments of the method’s stability and complexity.

Flora historica : or, The three seasons of the British parterre historically and botanically treated : with observations on planting, to secure a regular succession of flowers from the commencement of spring to the end of autumn /

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