Cognitive process modelling of controllers in en route air traffic control

In recent years, various efforts have been made in air traffic control (ATC) to maintain traffic safety and efficiency in the face of increasing air traffic demands. ATC is a complex process that depends to a large degree on human capabilities, and so understanding how controllers carry out their tasks is an important issue in the design and development of ATC systems. In particular, the human factor is considered to be a serious problem in ATC safety and has been identified as a causal factor in both major and minor incidents. There is, therefore, a need to analyse the mechanisms by which errors occur due to complex factors and to develop systems that can deal with these errors. From the cognitive process perspective, it is essential that system developers have an understanding of the more complex working processes that involve the cooperative work of multiple controllers. Distributed cognition is a methodological framework for analysing cognitive processes that span multiple actors mediated by technology. In this research, we attempt to analyse and model interactions that take place in en route ATC systems based on distributed cognition. We examine the functional problems in an ATC system from a human factors perspective, and conclude by identifying certain measures by which to address these problems. This research focuses on the analysis of air traffic controllers' tasks for en route ATC and modelling controllers' cognitive processes.

On discrimination algorithms for ill-posed problems with an application to magnetic tomography

In this paper we explore classification techniques for ill-posed problems. Two classes are linearly separable in some Hilbert space X if they can be separated by a hyperplane. We investigate stable separability, i.e. the case where we have a positive distance between two separating hyperplanes. When the data in the space Y is generated by a compact operator A applied to the system states ∈ X, we will show that in general we do not obtain stable separability in Y even if the problem in X is stably separable. In particular, we show this for the case where a nonlinear classification is generated from a non-convergent family of linear classes in X. We apply our results to the problem of quality control of fuel cells where we classify fuel cells according to their efficiency. We can potentially classify a fuel cell using either some external measured magnetic field or some internal current. However we cannot measure the current directly since we cannot access the fuel cell in operation. The first possibility is to apply discrimination techniques directly to the measured magnetic fields. The second approach first reconstructs currents and then carries out the classification on the current distributions. We show that both approaches need regularization and that the regularized classifications are not equivalent in general. Finally, we investigate a widely used linear classification algorithm Fisher's linear discriminant with respect to its ill-posedness when applied to data generated via a compact integral operator. We show that the method cannot stay stable when the number of measurement points becomes large.

Optimal linearization trajectories for tangent linear models

We examine differential equations where nonlinearity is a result of the advection part of the total derivative or the use of quadratic algebraic constraints between state variables (such as the ideal gas law). We show that these types of nonlinearity can be accounted for in the tangent linear model by a suitable choice of the linearization trajectory. Using this optimal linearization trajectory, we show that the tangent linear model can be used to reproduce the exact nonlinear error growth of perturbations for more than 200 days in a quasi-geostrophic model and more than (the equivalent of) 150 days in the Lorenz 96 model. We introduce an iterative method, purely based on tangent linear integrations, that converges to this optimal linearization trajectory. The main conclusion from this article is that this iterative method can be used to account for nonlinearity in estimation problems without using the nonlinear model. We demonstrate this by performing forecast sensitivity experiments in the Lorenz 96 model and show that we are able to estimate analysis increments that improve the two-day forecast using only four backward integrations with the tangent linear model. Copyright © 2011 Royal Meteorological Society

Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex

In this paper we study convergence of the L2-projection onto the space of polynomials up to degree p on a simplex in Rd, d >= 2. Optimal error estimates are established in the case of Sobolev regularity and illustrated on several numerical examples. The proof is based on the collapsed coordinate transform and the expansion into various polynomial bases involving Jacobi polynomials and their antiderivatives. The results of the present paper generalize corresponding estimates for cubes in Rd from [P. Houston, C. Schwab, E. Süli, Discontinuous hp-finite element methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 39 (2002), no. 6, 2133-2163].

Gradient recovery in adaptive finite-element methods for parabolic problems

We derive energy-norm a posteriori error bounds, using gradient recovery (ZZ) estimators to control the spatial error, for fully discrete schemes for the linear heat equation. This appears to be the �rst completely rigorous derivation of ZZ estimators for fully discrete schemes for evolution problems, without any restrictive assumption on the timestep size. An essential tool for the analysis is the elliptic reconstruction technique.Our theoretical results are backed with extensive numerical experimentation aimed at (a) testing the practical sharpness and asymptotic behaviour of the error estimator against the error, and (b) deriving an adaptive method based on our estimators. An extra novelty provided is an implementation of a coarsening error "preindicator", with a complete implementation guide in ALBERTA in the appendix.

A modified PNN algorithm with optimal PD modeling using the orthogonal least squares method

In this paper a modified algorithm is suggested for developing polynomial neural network (PNN) models. Optimal partial description (PD) modeling is introduced at each layer of the PNN expansion, a task accomplished using the orthogonal least squares (OLS) method. Based on the initial PD models determined by the polynomial order and the number of PD inputs, OLS selects the most significant regressor terms reducing the output error variance. The method produces PNN models exhibiting a high level of accuracy and superior generalization capabilities. Additionally, parsimonious models are obtained comprising a considerably smaller number of parameters compared to the ones generated by means of the conventional PNN algorithm. Three benchmark examples are elaborated, including modeling of the gas furnace process as well as the iris and wine classification problems. Extensive simulation results and comparison with other methods in the literature, demonstrate the effectiveness of the suggested modeling approach.

Sparse polynomial approximation in positive order Sobolev spaces with bounded mixed derivatives and applications to elliptic problems with random loading

In the present paper we study the approximation of functions with bounded mixed derivatives by sparse tensor product polynomials in positive order tensor product Sobolev spaces. We introduce a new sparse polynomial approximation operator which exhibits optimal convergence properties in L2 and tensorized View the MathML source simultaneously on a standard k-dimensional cube. In the special case k=2 the suggested approximation operator is also optimal in L2 and tensorized H1 (without essential boundary conditions). This allows to construct an optimal sparse p-version FEM with sparse piecewise continuous polynomial splines, reducing the number of unknowns from O(p2), needed for the full tensor product computation, to View the MathML source, required for the suggested sparse technique, preserving the same optimal convergence rate in terms of p. We apply this result to an elliptic differential equation and an elliptic integral equation with random loading and compute the covariances of the solutions with View the MathML source unknowns. Several numerical examples support the theoretical estimates.

From farmers’ perspective : pesticide use and pest control

Many studies have shown that farmers in developing countries often overuse pesticides and do not adopt safety practices. Policies and interventions to promote a safer use of pesticides are often based on a limited understanding of the farmers’ own perspective of pesticide use. This often results in ineffective policies and the persistence of significant pesticide-related health and environmental problems, especially in developing countries. This chapter explores potentials and limitations of different approaches to study pesticide use in agriculture from the farmers’ perspective. In contrast to the reductionist and mono-disciplinary approaches often adopted, this chapter calls for integrative methodological approaches to provide a realistic and thorough understanding of the farmers’ perspective on pesticide use and illustrates the added value of such an approach with three case studies of pesticide use in Iran, India, and Colombia.

Body-centric modelling, identification, and acceleration tracking control of a quadrotor UAV

This paper presents the mathematical development of a body-centric nonlinear dynamic model of a quadrotor UAV that is suitable for the development of biologically inspired navigation strategies. Analytical approximations are used to find an initial guess of the parameters of the nonlinear model, then parameter estimation methods are used to refine the model parameters using the data obtained from onboard sensors during flight. Due to the unstable nature of the quadrotor model, the identification process is performed with the system in closed-loop control of attitude angles. The obtained model parameters are validated using real unseen experimental data. Based on the identified model, a Linear-Quadratic (LQ) optimal tracker is designed to stabilize the quadrotor and facilitate its translational control by tracking body accelerations. The LQ tracker is tested on an experimental quadrotor UAV and the obtained results are a further means to validate the quality of the estimated model. The unique formulation of the control problem in the body frame makes the controller better suited for bio-inspired navigation and guidance strategies than conventional attitude or position based control systems that can be found in the existing literature.

Investigating music tempo as a feedback mechanism for closed-loop BCI control

The feedback mechanism used in a brain-computer interface (BCI) forms an integral part of the closed-loop learning process required for successful operation of a BCI. However, ultimate success of the BCI may be dependent upon the modality of the feedback used. This study explores the use of music tempo as a feedback mechanism in BCI and compares it to the more commonly used visual feedback mechanism. Three different feedback modalities are compared for a kinaesthetic motor imagery BCI: visual, auditory via music tempo, and a combined visual and auditory feedback modality. Visual feedback is provided via the position, on the y-axis, of a moving ball. In the music feedback condition, the tempo of a piece of continuously generated music is dynamically adjusted via a novel music-generation method. All the feedback mechanisms allowed users to learn to control the BCI. However, users were not able to maintain as stable control with the music tempo feedback condition as they could in the visual feedback and combined conditions. Additionally, the combined condition exhibited significantly less inter-user variability, suggesting that multi-modal feedback may lead to more robust results. Finally, common spatial patterns are used to identify participant-specific spatial filters for each of the feedback modalities. The mean optimal spatial filter obtained for the music feedback condition is observed to be more diffuse and weaker than the mean spatial filters obtained for the visual and combined feedback conditions.

A comparison of duality and energy a posteriori estimates for $\mathrm {L}_{\infty }(0,T;\mathrm {L}_2(\varOmega ))$ in parabolic problems

We use the elliptic reconstruction technique in combination with a duality approach to prove a posteriori error estimates for fully discrete backward Euler scheme for linear parabolic equations. As an application, we combine our result with the residual based estimators from the a posteriori estimation for elliptic problems to derive space-error indicators and thus a fully practical version of the estimators bounding the error in the $ \mathrm {L}_{\infty }(0,T;\mathrm {L}_2(\varOmega ))$ norm. These estimators, which are of optimal order, extend those introduced by Eriksson and Johnson in 1991 by taking into account the error induced by the mesh changes and allowing for a more flexible use of the elliptic estimators. For comparison with previous results we derive also an energy-based a posteriori estimate for the $ \mathrm {L}_{\infty }(0,T;\mathrm {L}_2(\varOmega ))$-error which simplifies a previous one given by Lakkis and Makridakis in 2006. We then compare both estimators (duality vs. energy) in practical situations and draw conclusions.

Reduced relative entropy techniques for a priori analysis of multiphase problems in elastodynamics

We give an a priori analysis of a semi-discrete discontinuous Galerkin scheme approximating solutions to a model of multiphase elastodynamics which involves an energy density depending not only on the strain but also the strain gradient. A key component in the analysis is the reduced relative entropy stability framework developed in Giesselmann (SIAM J Math Anal 46(5):3518–3539, 2014). The estimate we derive is optimal in the L∞(0,T;dG) norm for the strain and the L2(0,T;dG) norm for the velocity, where dG is an appropriate mesh dependent H1-like space.

Optimal infinity-quasiconformal immersions

For a Hamiltonian K ∈ C2(RN × n) and a map u:Ω ⊆ Rn − → RN, we consider the supremal functional (1) The “Euler−Lagrange” PDE associated to (1)is the quasilinear system (2) Here KP is the derivative and [ KP ] ⊥ is the projection on its nullspace. (1)and (2)are the fundamental objects of vector-valued Calculus of Variations in L∞ and first arose in recent work of the author [N. Katzourakis, J. Differ. Eqs. 253 (2012) 2123–2139; Commun. Partial Differ. Eqs. 39 (2014) 2091–2124]. Herein we apply our results to Geometric Analysis by choosing as K the dilation function which measures the deviation of u from being conformal. Our main result is that appropriately defined minimisers of (1)solve (2). Hence, PDE methods can be used to study optimised quasiconformal maps. Nonconvexity of K and appearance of interfaces where [ KP ] ⊥ is discontinuous cause extra difficulties. When n = N, this approach has previously been followed by Capogna−Raich ? and relates to Teichmüller’s theory. In particular, we disprove a conjecture appearing therein.

Mesh adaptation on the sphere using optimal transport and the numerical solution of a Monge-Ampère type equation

An equation of Monge-Ampère type has, for the first time, been solved numerically on the surface of the sphere in order to generate optimally transported (OT) meshes, equidistributed with respect to a monitor function. Optimal transport generates meshes that keep the same connectivity as the original mesh, making them suitable for r-adaptive simulations, in which the equations of motion can be solved in a moving frame of reference in order to avoid mapping the solution between old and new meshes and to avoid load balancing problems on parallel computers. The semi-implicit solution of the Monge-Ampère type equation involves a new linearisation of the Hessian term, and exponential maps are used to map from old to new meshes on the sphere. The determinant of the Hessian is evaluated as the change in volume between old and new mesh cells, rather than using numerical approximations to the gradients. OT meshes are generated to compare with centroidal Voronoi tesselations on the sphere and are found to have advantages and disadvantages; OT equidistribution is more accurate, the number of iterations to convergence is independent of the mesh size, face skewness is reduced and the connectivity does not change. However anisotropy is higher and the OT meshes are non-orthogonal. It is shown that optimal transport on the sphere leads to meshes that do not tangle. However, tangling can be introduced by numerical errors in calculating the gradient of the mesh potential. Methods for alleviating this problem are explored. Finally, OT meshes are generated using observed precipitation as a monitor function, in order to demonstrate the potential power of the technique.