Optimal Control of a Second Order Parabolic Heat Equation

In this paper, we are concerned with the optimal control boundary control of a second order parabolic heat equation. Using the results in [Evtushenko, 1997] and spatial central finite difference with diagonally implicit Runge-Kutta method (DIRK) is applied to solve the parabolic heat equation. The conjugate gradient method (CGM) is applied to solve the distributed control problem. Numerical results are reported.

Inverse space-dependent force problems for the wave equation

The determination of the displacement and the space-dependent force acting on a vibrating structure from measured final or time-average displacement observation is thoroughly investigated. Several aspects related to the existence and uniqueness of a solution of the linear but ill-posed inverse force problems are highlighted. After that, in order to capture the solution a variational formulation is proposed and the gradient of the least-squares functional that is minimized is rigorously and explicitly derived. Numerical results obtained using the Landweber method and the conjugate gradient method are presented and discussed illustrating the convergence of the iterative procedures for exact input data. Furthermore, for noisy data the semi-convergence phenomenon appears, as expected, and stability is restored by stopping the iterations according to the discrepancy principle criterion once the residual becomes close to the amount of noise. The present investigation will be significant to researchers concerned with wave propagation and control of vibrating structures.

Quality balancing for parallel adaptive FEM

We present a dynamic distributed load balancing algorithm for parallel, adaptive finite element simulations using preconditioned conjugate gradient solvers based on domain-decomposition. The load balancer is designed to maintain good partition aspect ratios. It can calculate a balancing flow using different versions of diffusion and a variant of breadth first search. Elements to be migrated are chosen according to a cost function aiming at the optimization of subdomain shapes. We show how to use information from the second step to guide the first. Experimental results using Bramble's preconditioner and comparisons to existing state-ot-the-art load balancers show the benefits of the construction.

Load balancing for parallel adaptive FEM

We present a dynamic distributed load balancing algorithm for parallel, adaptive finite element simulations using preconditioned conjugate gradient solvers based on domain-decomposition. The load balancer is designed to maintain good partition aspect ratios. It calculates a balancing flow using different versions of diffusion and a variant of breadth first search. Elements to be migrated are chosen according to a cost function aiming at the optimization of subdomain shapes. We show how to use information from the second step to guide the first. Experimental results using Bramble's preconditioner and comparisons to existing state-of-the-art balancers show the benefits of the construction.

Reconstruction of inclusions in photothermal imaging

Photothermal imaging allows to inspect the structure of composite materials by means of nondestructive tests. The surface of a medium is heated at a number of locations. The resulting temperature field is recorded on the same surface. Thermal waves are strongly damped. Robust schemes are needed to reconstruct the structure of the medium from the decaying time dependent temperature field. The inverse problem is formulated as a weighted optimization problem with a time dependent constraint. The inclusions buried in the medium and their material constants are the design variables. We propose an approximation scheme in two steps. First, Laplace transforms are used to generate an approximate optimization problem with a small number of stationary constraints. Then, we implement a descent strategy alternating topological derivative techniques to reconstruct the geometry of inclusions with gradient methods to identify their material parameters. Numerical simulations assess the effectivity of the technique.

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.

Hybrid topological derivative and gradient-based methods for electrical impedance tomography

We present a technique to reconstruct the electromagnetic properties of a medium or a set of objects buried inside it from boundary measurements when applying electric currents through a set of electrodes. The electromagnetic parameters may be recovered by means of a gradient method without a priori information on the background. The shape, location and size of objects, when present, are determined by a topological derivative-based iterative procedure. The combination of both strategies allows improved reconstructions of the objects and their properties, assuming a known background.

Evaluation of frozen ground conditions along a coastal topographic gradient at Byers Peninsula (Livingston Island, Antarctica) by geophysical and geoecological methods

Geophysical surveying and geoelectricalmethods are effective to study permafrost distribution and conditions in polar environments. Geoelectrical methods are particularly suited to study the spatial distribution of permafrost because of its high electrical resistivity in comparison with that of soil or rock above 0 °C. In the South Shetland Islands permafrost is considered to be discontinuous up to elevations of 20–40ma.s.l., changing to continuous at higher altitudes. There are no specific data about the distribution of permafrost in Byers Peninsula, in Livingston Island, which is the largest ice-free area in the South Shetland Islands. With the purpose of better understanding the occurrence of permanent frozen conditions in this area, a geophysical survey using an electrical resistivity tomography (ERT)methodologywas conducted during the January 2015 field season, combined with geomorphological and ecological studies. Three overlapping electrical resistivity tomographies of 78meach were done along the same profile which ran from the coast to the highest raised beaches. The three electrical resistivity tomographies are combined in an electrical resistivitymodel which represents the distribution of the electrical resistivity of the ground to depths of about 13malong 158m. Several patches of high electrical resistivity were found, and interpreted as patches of sporadic permafrost. The lower limits of sporadic to discontinuous permafrost in the area are confirmed by the presence of permafrost-related landforms nearby. There is a close correspondence between moss patches and permafrost patches along the geoelectrical transect.

Lateral buckling strength of simply supported LiteSteel beams subject to moment gradient effects

The flexural capacity of of a new cold-formed hollow flange channel section known as LiteSteel beam (LSB) is limited by lateral distortional buckling for intermediate spans, which is characterised by simultaneous lateral deflection, twist and web distortion. Recent research has developed suitable design rules for the member capacity of LSBs. However, they are limited to a uniform moment distribution that rarely exists in practice. Many steel design codes have adopted equivalent uniform moment distribution factors to accommodate the effect of non-uniform moment distributions in design. But they were derived mostly based on the data for conventional hot-rolled, doubly symmetric I-beams subject to lateral torsional buckling. The effect of moment distribution for LSBs, and the suitability of the current steel design code rules to include this effect for LSBs are not yet known. This paper presents the details of a research study based on finite element analyses of the lateral buckling strength of simply supported LSBs subject to moment gradient effects. It also presents the details of a number of LSB lateral buckling experiments undertaken to validate the results of finite element analyses. Finally, it discusses the suitability of the current design methods, and provides design recommendations for simply supported LSBs subject to moment gradient effects.

Exponentiated gradient algorithms for conditional random fields and max-margin Markov Networks

Log-linear and maximum-margin models are two commonly-used methods in supervised machine learning, and are frequently used in structured prediction problems. Efficient learning of parameters in these models is therefore an important problem, and becomes a key factor when learning from very large data sets. This paper describes exponentiated gradient (EG) algorithms for training such models, where EG updates are applied to the convex dual of either the log-linear or max-margin objective function; the dual in both the log-linear and max-margin cases corresponds to minimizing a convex function with simplex constraints. We study both batch and online variants of the algorithm, and provide rates of convergence for both cases. In the max-margin case, O(1/ε) EG updates are required to reach a given accuracy ε in the dual; in contrast, for log-linear models only O(log(1/ε)) updates are required. For both the max-margin and log-linear cases, our bounds suggest that the online EG algorithm requires a factor of n less computation to reach a desired accuracy than the batch EG algorithm, where n is the number of training examples. Our experiments confirm that the online algorithms are much faster than the batch algorithms in practice. We describe how the EG updates factor in a convenient way for structured prediction problems, allowing the algorithms to be efficiently applied to problems such as sequence learning or natural language parsing. We perform extensive evaluation of the algorithms, comparing them to L-BFGS and stochastic gradient descent for log-linear models, and to SVM-Struct for max-margin models. The algorithms are applied to a multi-class problem as well as to a more complex large-scale parsing task. In all these settings, the EG algorithms presented here outperform the other methods.

Does a 10-valent pneumococcal-Haemophilus influenzae protein D conjugate vaccine prevent respiratory exacerbations in children with recurrent protracted bacterial bronchitis, chronic suppurative lung disease and bronchiectasis : protocol for a randomised controlled trial

Background Recurrent protracted bacterial bronchitis (PBB), chronic suppurative lung disease (CSLD) and bronchiectasis are characterised by a chronic wet cough and are important causes of childhood respiratory morbidity globally. Haemophilus influenzae and Streptococcus pneumoniae are the most commonly associated pathogens. As respiratory exacerbations impair quality of life and may be associated with disease progression, we will determine if the novel 10-valent pneumococcal-Haemophilus influenzae protein D conjugate vaccine (PHiD-CV) reduces exacerbations in these children. Methods A multi-centre, parallel group, double-blind, randomised controlled trial in tertiary paediatric centres from three Australian cities is planned. Two hundred six children aged 18 months to 14 years with recurrent PBB, CSLD or bronchiectasis will be randomised to receive either two doses of PHiD-CV or control meningococcal (ACYW(135)) conjugate vaccine 2 months apart and followed for 12 months after the second vaccine dose. Randomisation will be stratified by site, age (<6 years and >= 6 years) and aetiology (recurrent PBB or CSLD/bronchiectasis). Clinical histories, respiratory status (including spirometry in children aged >= 6 years), nasopharyngeal and saliva swabs, and serum will be collected at baseline and at 2, 3, 8 and 14 months post-enrolment. Local and systemic reactions will be recorded on daily diaries for 7 and 30 days, respectively, following each vaccine dose and serious adverse events monitored throughout the trial. Fortnightly, parental contact will help record respiratory exacerbations. The primary outcome is the incidence of respiratory exacerbations in the 12 months following the second vaccine dose. Secondary outcomes include: nasopharyngeal carriage of H. influenzae and S. pneumoniae vaccine and vaccine-related serotypes; systemic and mucosal immune responses to H. influenzae proteins and S. pneumoniae vaccine and vaccine-related serotypes; impact upon lung function in children aged >= 6 years; and vaccine safety. Discussion As H. influenzae is the most common bacterial pathogen associated with these chronic respiratory diseases in children, a novel pneumococcal conjugate vaccine that also impacts upon H. influenzae and helps prevent respiratory exacerbations would assist clinical management with potential short- and long-term health benefits. Our study will be the first to assess vaccine efficacy targeting H. influenzae in children with recurrent PBB, CSLD and bronchiectasis.

Effectiveness of 7-valent pneumococcal conjugate vaccine against radiologically diagnosed pneumonia in indigenous infants in Australia

Objective To evaluate the effectiveness of the 7-valent pneumococcal conjugate vaccine (PCV7) in preventing pneumonia, diagnosed radiologically according to World Health Organization (WHO) criteria, among indigenous infants in the Northern Territory of Australia. Methods We conducted a historical cohort study of consecutive indigenous birth cohorts between 1 April 1998 and 28 February 2005. Children were followed up to 18 months of age. The PCV7 programme commenced on 1 June 2001. All chest X-rays taken within 3 days of any hospitalization were assessed. The primary endpoint was a first episode of WHO-defined pneumonia requiring hospitalization. Cox proportional hazards models were used to compare disease incidence. Findings There were 526 pneumonia events among 10 600 children - an incidence of 3.3 per 1000 child-months; 183 episodes (34.8%) occurred before 5 months of age and 247 (47.0%) by 7 months. Of the children studied, 27% had received 3 doses of vaccine by 7 months of age. Hazard ratios for endpoint pneumonia were 1.01 for 1 versus 0 doses; 1.03 for 2 versus 0 doses; and 0.84 for 3 versus 0 doses. Conclusion There was limited evidence that PCV7 reduced the incidence of radiologically confirmed pneumonia among Northern Territory indigenous infants, although there was a non-significant trend towards an effect after receipt of the third dose. These findings might be explained by lack of timely vaccination and/or occurrence of disease at an early age. Additionally, the relative contribution of vaccine-type pneumococcus to severe pneumonia in a setting where multiple other pathogens are prevalent may differ with respect to other settings where vaccine efficacy has been clearly established.