The measurement of applied forces during anterior single rod surgical correction of adolescent idiopathic scoliosis

INTRODUCTION. Following anterior thoracoscopic instrumentation and fusion for the treatment of thoracic AIS, implant related complications have been reported as high as 20.8%. Currently the magnitudes of the forces applied to the spine during anterior scoliosis surgery are unknown. The aim of this study was to measure the segmental compressive forces applied during anterior single rod instrumentation in a series of adolescent idiopathic scoliosis patients. METHODS. A force transducer was designed, constructed and retrofitted to a surgical cable compression tool, routinely used to apply segmental compression during anterior scoliosis correction. Transducer output was continuously logged during the compression of each spinal joint, the output at completion converted to an applied compression force using calibration data. The angle between adjacent vertebral body screws was also measured on intra-operative frontal plane fluoroscope images taken both before and after each joint compression. The difference in angle between the two images was calculated as an estimate for the achieved correction at each spinal joint. RESULTS. Force measurements were obtained for 15 scoliosis patients (Aged 11-19 years) with single thoracic curves (Cobb angles 47˚- 67˚). In total, 95 spinal joints were instrumented. The average force applied for a single joint was 540 N (± 229 N)ranging between 88 N and 1018 N. Experimental error in the force measurement, determined from transducer calibration was ± 43 N. A trend for higher forces applied at joints close to the apex of the scoliosis was observed. The average joint correction angle measured by fluoroscope imaging was 4.8˚ (±2.6˚, range 0˚-12.6˚). CONCLUSION. This study has quantified in-vivo, the intra-operative correction forces applied by the surgeon during anterior single rod instrumentation. This data provides a useful contribution towards an improved understanding of the biomechanics of scoliosis correction. In particular, this data will be used as input for developing patient-specific finite element simulations of scoliosis correction surgery.

A Stochastic View of Optimal Regret through Minimax Duality

We study the regret of optimal strategies for online convex optimization games. Using von Neumann's minimax theorem, we show that the optimal regret in this adversarial setting is closely related to the behavior of the empirical minimization algorithm in a stochastic process setting: it is equal to the maximum, over joint distributions of the adversary's action sequence, of the difference between a sum of minimal expected losses and the minimal empirical loss. We show that the optimal regret has a natural geometric interpretation, since it can be viewed as the gap in Jensen's inequality for a concave functional--the minimizer over the player's actions of expected loss--defined on a set of probability distributions. We use this expression to obtain upper and lower bounds on the regret of an optimal strategy for a variety of online learning problems. Our method provides upper bounds without the need to construct a learning algorithm; the lower bounds provide explicit optimal strategies for the adversary. Peter L. Bartlett, Alexander Rakhlin

Mechanical properties of cold-formed steels at elevated temperatures

Mechanical properties have an important role in the fire safety design of cold-formed steel structures due to the rapid reduction in mechanical properties such as yield strength and elastic modulus under fire conditions and associated reduction to the load carrying capacities. Hence there is a need to fully understand the deterioration characteristics of yield strength and elastic modulus of cold-formed steels at elevated temperatures. Although past research has produced useful experimental data on the mechanical properties of cold-formed steels at elevated temperatures, such data do not yet cover different cold-formed steel grades and thicknesses. Therefore, an experimental study was undertaken to investigate the elevated temperature mechanical properties of two low and high strength steels with two thicknesses that are commonly used in Australia. Tensile coupon tests were undertaken using a steady state test method for temperatures in the range 20–700 °C. Test results were compared with the currently available reduction factors for yield strength and elastic modulus, and stress–strain curves, based on which further improvements were made. For this purpose, test results of many other cold-formed steels were also used based on other similar studies undertaken at the Queensland University of Technology. Improved equations were developed to predict the yield strength and elastic modulus reduction factors and stress–strain curves of a range of cold-formed steel grades and thicknesses used in Australia. This paper presents the results of this experimental study, comparisons with the results of past research and steel design standards, and the new predictive equations.

Soil carbon sequestration rates and associated economic costs for farming systems of south-eastern Australia

Soil organic carbon (C) sequestration rates based on the Intergovernmental Panel for Climate Change (IPCC) methodology were combined with local economic data to simulate the economic potential for C sequestration in response to conservation tillage in the six agro-ecological zones within the Southern Region of the Australian grains industry. The net C sequestration rate over 20 years for the Southern Region (which includes discounting for associated greenhouse gases) is estimated to be 3.6 or 6.3 Mg C/ha after converting to either minimum or no-tillage practices, respectively, with no-till practices estimated to return 75% more carbon on average than minimum tillage. The highest net gains in C per ha are realised when converting from conventional to no-tillage practices in the high-activity clay soils of the High Rainfall and Wimmera agro-ecological zones. On the basis of total area available for change, the Slopes agro-ecological zone offers the highest net returns, potentially sequestering an additional 7.1 Mt C under no-tillage scenario over 20 years. The economic analysis was summarised as C supply curves for each of the 6 zones expressing the total additional C accumulated over 20 years for a price per t C sequestered ranging from zero to AU$200. For a price of $50/Mg C, a total of 427 000 Mg C would be sequestered over 20 years across the Southern Region, <5% of the simulated C sequestration potential of 9.1 Mt for the region. The Wimmera and Mid-North offer the largest gains in C under minimum tillage over 20 years of all zones for all C prices. For the no-tillage scenario, for a price of $50/Mg C, 1.74 Mt C would be sequestered over 20 years across the Southern Region, <10% of the simulated C sequestration potential of 18.6 Mt for the region over 20 years. The Slopes agro-ecological zone offers the best return in C over 20 years under no-tillage for all C prices. The Mallee offers the least return for both minimum and no-tillage scenarios. At a price of $200/Mg C, the transition from conventional tillage to minimum or no-tillage practices will only realise 19% and 33%, respectively, of the total biogeochemical sequestration potential of crop and pasture systems of the Southern Region over a 20-year period.

A restrike waveform predictive model for shunt capacitor bank switching with point-on-wave recommendation

Circuit-breakers (CBs) are subject to electrical stresses with restrikes during capacitor bank operation. Stresses are caused by the overvoltages across CBs, the interrupting currents and the rate of rise of recovery voltage (RRRV). Such electrical stresses also depend on the types of system grounding and the types of dielectric strength curves. The aim of this study is to demonstrate a restrike waveform predictive model for a SF6 CB that considered the types of system grounding: grounded and non-grounded and the computation accuracy comparison on the application of the cold withstand dielectric strength and the hot recovery dielectric strength curve including the POW (point-on-wave) recommendations to make an assessment of increasing the CB remaining life. The simulation of SF6 CB stresses in a typical 400 kV system was undertaken and the results in the applications are presented. The simulated restrike waveforms produced with the identified features using wavelet transform can be used for restrike diagnostic algorithm development with wavelet transform to locate a substation with breaker restrikes. This study found that the hot withstand dielectric strength curve has less magnitude than the cold withstand dielectric strength curve for restrike simulation results. Computation accuracy improved with the hot withstand dielectric strength and POW controlled switching can increase the life for a SF6 CB.

Path planning, guidance and control for a UAV forced landing

A forced landing is an unscheduled event in flight requiring an emergency landing, and is most commonly attributed to engine failure, failure of avionics or adverse weather. Since the ability to conduct a successful forced landing is the primary indicator for safety in the aviation industry, automating this capability for unmanned aerial vehicles (UAVs) will help facilitate their integration into, and subsequent routine operations over civilian airspace. Currently, there is no commercial system available to perform this task; however, a team at the Australian Research Centre for Aerospace Automation (ARCAA) is working towards developing such an automated forced landing system. This system, codenamed Flight Guardian, will operate onboard the aircraft and use machine vision for site identification, artificial intelligence for data assessment and evaluation, and path planning, guidance and control techniques to actualize the landing. This thesis focuses on research specific to the third category, and presents the design, testing and evaluation of a Trajectory Generation and Guidance System (TGGS) that navigates the aircraft to land at a chosen site, following an engine failure. Firstly, two algorithms are developed that adapts manned aircraft forced landing techniques to suit the UAV planning problem. Algorithm 1 allows the UAV to select a route (from a library) based on a fixed glide range and the ambient wind conditions, while Algorithm 2 uses a series of adjustable waypoints to cater for changing winds. A comparison of both algorithms in over 200 simulated forced landings found that using Algorithm 2, twice as many landings were within the designated area, with an average lateral miss distance of 200 m at the aimpoint. These results present a baseline for further refinements to the planning algorithms. A significant contribution is seen in the design of the 3-D Dubins Curves planning algorithm, which extends the elementary concepts underlying 2-D Dubins paths to account for powerless flight in three dimensions. This has also resulted in the development of new methods in testing for path traversability, in losing excess altitude, and in the actual path formation to ensure aircraft stability. Simulations using this algorithm have demonstrated lateral and vertical miss distances of under 20 m at the approach point, in wind speeds of up to 9 m/s. This is greater than a tenfold improvement on Algorithm 2 and emulates the performance of manned, powered aircraft. The lateral guidance algorithm originally developed by Park, Deyst, and How (2007) is enhanced to include wind information in the guidance logic. A simple assumption is also made that reduces the complexity of the algorithm in following a circular path, yet without sacrificing performance. Finally, a specific method of supplying the correct turning direction is also used. Simulations have shown that this new algorithm, named the Enhanced Nonlinear Guidance (ENG) algorithm, performs much better in changing winds, with cross-track errors at the approach point within 2 m, compared to over 10 m using Park's algorithm. A fourth contribution is made in designing the Flight Path Following Guidance (FPFG) algorithm, which uses path angle calculations and the MacCready theory to determine the optimal speed to fly in winds. This algorithm also uses proportional integral- derivative (PID) gain schedules to finely tune the tracking accuracies, and has demonstrated in simulation vertical miss distances of under 2 m in changing winds. A fifth contribution is made in designing the Modified Proportional Navigation (MPN) algorithm, which uses principles from proportional navigation and the ENG algorithm, as well as methods specifically its own, to calculate the required pitch to fly. This algorithm is robust to wind changes, and is easily adaptable to any aircraft type. Tracking accuracies obtained with this algorithm are also comparable to those obtained using the FPFG algorithm. For all three preceding guidance algorithms, a novel method utilising the geometric and time relationship between aircraft and path is also employed to ensure that the aircraft is still able to track the desired path to completion in strong winds, while remaining stabilised. Finally, a derived contribution is made in modifying the 3-D Dubins Curves algorithm to suit helicopter flight dynamics. This modification allows a helicopter to autonomously track both stationary and moving targets in flight, and is highly advantageous for applications such as traffic surveillance, police pursuit, security or payload delivery. Each of these achievements serves to enhance the on-board autonomy and safety of a UAV, which in turn will help facilitate the integration of UAVs into civilian airspace for a wider appreciation of the good that they can provide. The automated UAV forced landing planning and guidance strategies presented in this thesis will allow the progression of this technology from the design and developmental stages, through to a prototype system that can demonstrate its effectiveness to the UAV research and operations community.

Convexity, Classification, and Risk Bounds

Many of the classification algorithms developed in the machine learning literature, including the support vector machine and boosting, can be viewed as minimum contrast methods that minimize a convex surrogate of the 0–1 loss function. The convexity makes these algorithms computationally efficient. The use of a surrogate, however, has statistical consequences that must be balanced against the computational virtues of convexity. To study these issues, we provide a general quantitative relationship between the risk as assessed using the 0–1 loss and the risk as assessed using any nonnegative surrogate loss function. We show that this relationship gives nontrivial upper bounds on excess risk under the weakest possible condition on the loss function—that it satisfies a pointwise form of Fisher consistency for classification. The relationship is based on a simple variational transformation of the loss function that is easy to compute in many applications. We also present a refined version of this result in the case of low noise, and show that in this case, strictly convex loss functions lead to faster rates of convergence of the risk than would be implied by standard uniform convergence arguments. Finally, we present applications of our results to the estimation of convergence rates in function classes that are scaled convex hulls of a finite-dimensional base class, with a variety of commonly used loss functions.

Learning the kernel matrix with semidefinite programming

Kernel-based learning algorithms work by embedding the data into a Euclidean space, and then searching for linear relations among the embedded data points. The embedding is performed implicitly, by specifying the inner products between each pair of points in the embedding space. This information is contained in the so-called kernel matrix, a symmetric and positive semidefinite matrix that encodes the relative positions of all points. Specifying this matrix amounts to specifying the geometry of the embedding space and inducing a notion of similarity in the input space - classical model selection problems in machine learning. In this paper we show how the kernel matrix can be learned from data via semidefinite programming (SDP) techniques. When applied to a kernel matrix associated with both training and test data this gives a powerful transductive algorithm -using the labeled part of the data one can learn an embedding also for the unlabeled part. The similarity between test points is inferred from training points and their labels. Importantly, these learning problems are convex, so we obtain a method for learning both the model class and the function without local minima. Furthermore, this approach leads directly to a convex method for learning the 2-norm soft margin parameter in support vector machines, solving an important open problem.

Fast rates for estimation error and oracle inequalities for model section

We consider complexity penalization methods for model selection. These methods aim to choose a model to optimally trade off estimation and approximation errors by minimizing the sum of an empirical risk term and a complexity penalty. It is well known that if we use a bound on the maximal deviation between empirical and true risks as a complexity penalty, then the risk of our choice is no more than the approximation error plus twice the complexity penalty. There are many cases, however, where complexity penalties like this give loose upper bounds on the estimation error. In particular, if we choose a function from a suitably simple convex function class with a strictly convex loss function, then the estimation error (the difference between the risk of the empirical risk minimizer and the minimal risk in the class) approaches zero at a faster rate than the maximal deviation between empirical and true risks. In this paper, we address the question of whether it is possible to design a complexity penalized model selection method for these situations. We show that, provided the sequence of models is ordered by inclusion, in these cases we can use tight upper bounds on estimation error as a complexity penalty. Surprisingly, this is the case even in situations when the difference between the empirical risk and true risk (and indeed the error of any estimate of the approximation error) decreases much more slowly than the complexity penalty. We give an oracle inequality showing that the resulting model selection method chooses a function with risk no more than the approximation error plus a constant times the complexity penalty.

Local Rademacher complexities

We propose new bounds on the error of learning algorithms in terms of a data-dependent notion of complexity. The estimates we establish give optimal rates and are based on a local and empirical version of Rademacher averages, in the sense that the Rademacher averages are computed from the data, on a subset of functions with small empirical error. We present some applications to classification and prediction with convex function classes, and with kernel classes in particular.

Classification with a reject option using a hinge loss

We consider the problem of binary classification where the classifier can, for a particular cost, choose not to classify an observation. Just as in the conventional classification problem, minimization of the sample average of the cost is a difficult optimization problem. As an alternative, we propose the optimization of a certain convex loss function φ, analogous to the hinge loss used in support vector machines (SVMs). Its convexity ensures that the sample average of this surrogate loss can be efficiently minimized. We study its statistical properties. We show that minimizing the expected surrogate loss—the φ-risk—also minimizes the risk. We also study the rate at which the φ-risk approaches its minimum value. We show that fast rates are possible when the conditional probability P(Y=1|X) is unlikely to be close to certain critical values.

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.

Sparseness vs estimating conditional probabilities : some asymptotic results

One of the nice properties of kernel classifiers such as SVMs is that they often produce sparse solutions. However, the decision functions of these classifiers cannot always be used to estimate the conditional probability of the class label. We investigate the relationship between these two properties and show that these are intimately related: sparseness does not occur when the conditional probabilities can be unambiguously estimated. We consider a family of convex loss functions and derive sharp asymptotic results for the fraction of data that becomes support vectors. This enables us to characterize the exact trade-off between sparseness and the ability to estimate conditional probabilities for these loss functions.

Adaptive online gradient descent

We study the rates of growth of the regret in online convex optimization. First, we show that a simple extension of the algorithm of Hazan et al eliminates the need for a priori knowledge of the lower bound on the second derivatives of the observed functions. We then provide an algorithm, Adaptive Online Gradient Descent, which interpolates between the results of Zinkevich for linear functions and of Hazan et al for strongly convex functions, achieving intermediate rates between [square root T] and [log T]. Furthermore, we show strong optimality of the algorithm. Finally, we provide an extension of our results to general norms.

Learning the Kernel Matrix with Semi-Definite Programming

Kernel-based learning algorithms work by embedding the data into a Euclidean space, and then searching for linear relations among the embedded data points. The embedding is performed implicitly, by specifying the inner products between each pair of points in the embedding space. This information is contained in the so-called kernel matrix, a symmetric and positive definite matrix that encodes the relative positions of all points. Specifying this matrix amounts to specifying the geometry of the embedding space and inducing a notion of similarity in the input space -- classical model selection problems in machine learning. In this paper we show how the kernel matrix can be learned from data via semi-definite programming (SDP) techniques. When applied to a kernel matrix associated with both training and test data this gives a powerful transductive algorithm -- using the labelled part of the data one can learn an embedding also for the unlabelled part. The similarity between test points is inferred from training points and their labels. Importantly, these learning problems are convex, so we obtain a method for learning both the model class and the function without local minima. Furthermore, this approach leads directly to a convex method to learn the 2-norm soft margin parameter in support vector machines, solving another important open problem. Finally, the novel approach presented in the paper is supported by positive empirical results.