Exploiting uncertainty in nonlinear stochastic control problem

This work introduces a novel inversion-based neurocontroller for solving control problems involving uncertain nonlinear systems which could also compensate for multi-valued systems. The approach uses recent developments in neural networks, especially in the context of modelling statistical distributions, which are applied to forward and inverse plant models. Provided that certain conditions are met, an estimate of the intrinsic uncertainty for the outputs of neural networks can be obtained using the statistical properties of networks. More generally, multicomponent distributions can be modelled by the mixture density network. Based on importance sampling from these distributions a novel robust inverse control approach is obtained. This importance sampling provides a structured and principled approach to constrain the complexity of the search space for the ideal control law. The developed methodology circumvents the dynamic programming problem by using the predicted neural network uncertainty to localise the possible control solutions to consider. Convergence of the output error for the proposed control method is verified by using a Lyapunov function. Several simulation examples are provided to demonstrate the efficiency of the developed control method. The manner in which such a method is extended to nonlinear multi-variable systems with different delays between the input-output pairs is considered and demonstrated through simulation examples.

An examination of organisational issues in third sector organisations which undertake nonviolent direct action

This thesis is an examination of organisational issues faced by Third Sector organisations which undertake nonviolent direct action. A case study methodology is employed and data gathered from four organisations: Earth First!; genetiX Snowball; Greenpeace; and Trident Ploughshares. The argument commences with a review of the literature which shows that little is known of the organising of nonviolent direct action. Operational definitions of 'organisation' and 'nonviolent direct action' are drawn from the literature. 'Organisation' is conceptualised using new institutionalism. 'Nonviolent direct action' is conceptualised using new social movement theory. These concepts inform the case study methodology in the choice of case, the organisations selected and the data gathering tools. Most data were gathered by semi-structured interview and participant observation. The research findings result from theory-building arising from thick descriptions of the case in the four organisations. The findings suggest that nonviolent direct action is qualitatively different from terrorism or violence. Although there is much diversity in philosophies of nonviolence, the practice of nonviolent direct action has much in common across the four organisations. The argument is that nonviolent direct action is an institution. The findings also suggest that new institutionalism is a fruitful approach to studies of these organisations. Along with nonviolent direct action, three other institutions are identified: 'rules'; consensus decision-making; and 'affinity groups'. An unanticipated finding is how the four organisations are instances of innovation. Tentative theory is developed which brings together the seemingly incompatible concepts of institutions and innovation. The theory suggests preconditions and then stages in the development of new organisational forms in new social movements: innovation. The three pre-conditions are: the existence of an institutional field; an 'institution-broker' with access to different domains; and a shared 'problem' to resolve. The three stages are: unlocking existing knowledge and practice; bridging different domains of practice or different fields to add, develop or translocate those practices; and establishing those practices within their new combinations or novel locations. Participants are able to move into and between these new organisational forms because they consist of familiar and habitual institutional behaviour.

Evolution of optical pulses in fiber lines with lumped nonlinear devices as a mapping problem

We analyze the steady-state propagation of optical pulses in fiber transmission systems with lumped nonlinear optical devices (NODs) placed periodically in the line. For the first time to our knowledge, a theoretical model is developed to describe the transmission regime with a quasilinear pulse evolution along the transmission line and the point action of NODs. We formulate the mapping problem for pulse propagation in a unit cell of the line and show that in the particular application to nonlinear optical loop mirrors, the steady-state pulse characteristics predicted by the theory accurately reproduce the results of direct numerical simulations.

A comparative study on applying the method of fundamental solutions to the backward heat conduction problem

We investigate an application of the method of fundamental solutions (MFS) to the backward heat conduction problem (BHCP). We extend the MFS in Johansson and Lesnic (2008) [5] and Johansson et al. (in press) [6] proposed for one and two-dimensional direct heat conduction problems, respectively, with the sources placed outside the space domain of interest. Theoretical properties of the method, as well as numerical investigations, are included, showing that accurate and stable results can be obtained efficiently with small computational cost.

Fast reconstruction of harmonic functions from Cauchy data using integral equation techniques

We consider the problem of stable determination of a harmonic function from knowledge of the solution and its normal derivative on a part of the boundary of the (bounded) solution domain. The alternating method is a procedure to generate an approximation to the harmonic function from such Cauchy data and we investigate a numerical implementation of this procedure based on Fredholm integral equations and Nyström discretization schemes, which makes it possible to perform a large number of iterations (millions) with minor computational cost (seconds) and high accuracy. Moreover, the original problem is rewritten as a fixed point equation on the boundary, and various other direct regularization techniques are discussed to solve that equation. We also discuss how knowledge of the smoothness of the data can be used to further improve the accuracy. Numerical examples are presented showing that accurate approximations of both the solution and its normal derivative can be obtained with much less computational time than in previous works.

An alternating boundary integral based method for a Cauchy problem for the Laplace equation in semi-infinite regions

We consider a Cauchy problem for the Laplace equation in a two-dimensional semi-infinite region with a bounded inclusion, i.e. the region is the intersection between a half-plane and the exterior of a bounded closed curve contained in the half-plane. The Cauchy data are given on the unbounded part of the boundary of the region and the aim is to construct the solution on the boundary of the inclusion. In 1989, Kozlov and Maz'ya [10] proposed an alternating iterative method for solving Cauchy problems for general strongly elliptic and formally self-adjoint systems in bounded domains. We extend their approach to our setting and in each iteration step mixed boundary value problems for the Laplace equation in the semi-infinite region are solved. Well-posedness of these mixed problems are investigated and convergence of the alternating procedure is examined. For the numerical implementation an efficient boundary integral equation method is proposed, based on the indirect variant of the boundary integral equation approach. The mixed problems are reduced to integral equations over the (bounded) boundary of the inclusion. Numerical examples are included showing the feasibility of the proposed method.

An alternating potential based approach for a Cauchy problem for the Laplace equation in a planar domain with a cut

We consider a Cauchy problem for the Laplace equation in a bounded region containing a cut, where the region is formed by removing a sufficiently smooth arc (the cut) from a bounded simply connected domain D. The aim is to reconstruct the solution on the cut from the values of the solution and its normal derivative on the boundary of the domain D. We propose an alternating iterative method which involves solving direct mixed problems for the Laplace operator in the same region. These mixed problems have either a Dirichlet or a Neumann boundary condition imposed on the cut and are solved by a potential approach. Each of these mixed problems is reduced to a system of integral equations of the first kind with logarithmic and hypersingular kernels and at most a square root singularity in the densities at the endpoints of the cut. The full discretization of the direct problems is realized by a trigonometric quadrature method which has super-algebraic convergence. The numerical examples presented illustrate the feasibility of the proposed method.

ICT diffusion and foreign direct investment:a comparative study between Asia-Pacific and the Middle Eastern economies

This chapter investigates the impact of inward and outward FDI on ICT diffusion in the Asia-Pacific and Middle East regions for the period 1996-2008. The results indicate that while inward FDI has generally had a positive and significant impact on ICT diffusion in Asia-Pacific economies, its impact on the Middle Eastern countries has been detrimental. In contrast, the results of this study also show that outward FDI has had, in general, the inverse effect, it has been in general positive and significant for the Middle East countries but insignificant for Asia-Pacific economies.

3D reconstruction of complex dielectric function of the glass during the femtosecond micro-fabrication

We measure complex amplitude of scattered wave in the far field, and justify theoretically and numerically solution of the inverse scattering problem. This allows single-shot reconstructing of dielectric function distribution during direct femtosecond laser micro-fabrication.

Evolution of optical pulses in fiber lines with lumped nonlinear devices as a mapping problem

We analyze the steady-state propagation of optical pulses in fiber transmission systems with lumped nonlinear optical devices (NODs) placed periodically in the line. For the first time to our knowledge, a theoretical model is developed to describe the transmission regime with a quasilinear pulse evolution along the transmission line and the point action of NODs. We formulate the mapping problem for pulse propagation in a unit cell of the line and show that in the particular application to nonlinear optical loop mirrors, the steady-state pulse characteristics predicted by the theory accurately reproduce the results of direct numerical simulations. © 2005 Springer Science+Business Media, Inc.

3D reconstruction of the complex dielectric function of glass during femtosecond laser micro-fabrication

We report on a new technique to reconstruct the 3D dielectric function change in transparent dielectric materials and the application of the technique for on-line monitoring of refractive index modification in BK7 glass during direct femtosecond laser microfabrication. The complex optical field scattered from the modified region is measured using two-beam, single-shot interferogram and the distribution of the modified refractive index is reconstructed by numerically solving the inverse scattering problem in Born approximation. The optical configuration suggested is further development of digital holographic microscopy. It takes advantage of high spatial resolution and almost the same optical paths for both interfering beams, and allows ultrafast time resolution. © Springer Science+Business Media, LLC. 2011.

Digital signal processing based on inverse scattering transform

Through numerical modeling, we illustrate the possibility of a new approach to digital signal processing in coherent optical communications based on the application of the so-called inverse scattering transform. Considering without loss of generality a fiber link with normal dispersion and quadrature phase shift keying signal modulation, we demonstrate how an initial information pattern can be recovered (without direct backward propagation) through the calculation of nonlinear spectral data of the received optical signal. © 2013 Optical Society of America.

3D reconstruction of complex dielectric function of the glass during the femtosecond micro-fabrication

We measure complex amplitude of scattered wave in the far field, and justify theoretically and numerically solution of the inverse scattering problem. This allows single-shot reconstructing of dielectric function distribution during direct femtosecond laser micro-fabrication.

Diabetic retinopathy and blockade of the renin–angiotensin system:new data from the DIRECT study programme

The pathogenesis and medical management of diabetic retinopathy is reviewed. The importance of good control of blood glucose and blood pressure remain key elements in the prevention and treatment of diabetic retinopathy, and a number of specific metabolic pathways have been identified that may be useful additional targets for therapeutic intervention. Trial data, however, aimed specifically to answer the questions of optimum medical management are limited, so the DIRECT study of renin-angiotensin blockade using oral candesartan 32 mg daily is a welcome addition to our knowledge. This arose from the promising improvement of retinopathy outcomes in the EUCLID study of lisinopril in type I diabetes. In DIRECT, 5 years of candesartan treatment in type I diabetes reduced the incidence of retinopathy by two or more steps (EDTRS) in severity by 18% (P = 0.0508) and, in a post hoc analysis, reduced the incidence of retinopathy by three-step progression by 35% (P = 0.034). In type I diabetes patients there was no effect on progression of established retinopathy. In contrast, in type II diabetes, 5 years of candesartan treatment resulted in 34% regression of retinopathy (P ≤0.009). Importantly, an overall significant change towards less-severe retinopathy was noted in both type I and II diabetes (P0.03). Although there is still no absolute proof that these effects were specific to RAS blockade, or just an effect of lower blood pressure, it is reasonable to conclude that candesartan has earned a place in the medical management of diabetic retinopathy, to prevent the problem in type I diabetes and to treat the early stages in type II diabetes. © 2010 Macmillan Publishers Limited All rights reserved.