Optimal strategies and minimax lower bounds for online convex games

A number of learning problems can be cast as an Online Convex Game: on each round, a learner makes a prediction x from a convex set, the environment plays a loss function f, and the learner’s long-term goal is to minimize regret. Algorithms have been proposed by Zinkevich, when f is assumed to be convex, and Hazan et al., when f is assumed to be strongly convex, that have provably low regret. We consider these two settings and analyze such games from a minimax perspective, proving minimax strategies and lower bounds in each case. These results prove that the existing algorithms are essentially optimal.

Cryptanalysis of the convex hull click human identification protocol

Recently, a convex hull-based human identification protocol was proposed by Sobrado and Birget, whose steps can be performed by humans without additional aid. The main part of the protocol involves the user mentally forming a convex hull of secret icons in a set of graphical icons and then clicking randomly within this convex hull. While some rudimentary security issues of this protocol have been discussed, a comprehensive security analysis has been lacking. In this paper, we analyze the security of this convex hull-based protocol. In particular, we show two probabilistic attacks that reveal the user’s secret after the observation of only a handful of authentication sessions. These attacks can be efficiently implemented as their time and space complexities are considerably less than brute force attack. We show that while the first attack can be mitigated through appropriately chosen values of system parameters, the second attack succeeds with a non-negligible probability even with large system parameter values that cross the threshold of usability.

Cryptanalysis of the convex hull click human identification protocol

Recently a convex hull based human identification protocol was proposed by Sobrado and Birget, whose steps can be performed by humans without additional aid. The main part of the protocol involves the user mentally forming a convex hull of secret icons in a set of graphical icons and then clicking randomly within this convex hull. In this paper we show two efficient probabilistic attacks on this protocol which reveal the user’s secret after the observation of only a handful of authentication sessions. We show that while the first attack can be mitigated through appropriately chosen values of system parameters, the second attack succeeds with a non-negligible probability even with large system parameter values which cross the threshold of usability.

Matching image sets via adaptive multi convex hull

Traditional nearest points methods use all the samples in an image set to construct a single convex or affine hull model for classification. However, strong artificial features and noisy data may be generated from combinations of training samples when significant intra-class variations and/or noise occur in the image set. Existing multi-model approaches extract local models by clustering each image set individually only once, with fixed clusters used for matching with various image sets. This may not be optimal for discrimination, as undesirable environmental conditions (eg. illumination and pose variations) may result in the two closest clusters representing different characteristics of an object (eg. frontal face being compared to non-frontal face). To address the above problem, we propose a novel approach to enhance nearest points based methods by integrating affine/convex hull classification with an adapted multi-model approach. We first extract multiple local convex hulls from a query image set via maximum margin clustering to diminish the artificial variations and constrain the noise in local convex hulls. We then propose adaptive reference clustering (ARC) to constrain the clustering of each gallery image set by forcing the clusters to have resemblance to the clusters in the query image set. By applying ARC, noisy clusters in the query set can be discarded. Experiments on Honda, MoBo and ETH-80 datasets show that the proposed method outperforms single model approaches and other recent techniques, such as Sparse Approximated Nearest Points, Mutual Subspace Method and Manifold Discriminant Analysis.

Separable spatiotemporal priors for convex reconstruction of time-varying 3D point clouds

Reconstructing 3D motion data is highly under-constrained due to several common sources of data loss during measurement, such as projection, occlusion, or miscorrespondence. We present a statistical model of 3D motion data, based on the Kronecker structure of the spatiotemporal covariance of natural motion, as a prior on 3D motion. This prior is expressed as a matrix normal distribution, composed of separable and compact row and column covariances. We relate the marginals of the distribution to the shape, trajectory, and shape-trajectory models of prior art. When the marginal shape distribution is not available from training data, we show how placing a hierarchical prior over shapes results in a convex MAP solution in terms of the trace-norm. The matrix normal distribution, fit to a single sequence, outperforms state-of-the-art methods at reconstructing 3D motion data in the presence of significant data loss, while providing covariance estimates of the imputed points.

Foil rolling : a new interpretation of experimental results

This paper explores a new interpretation of experiments on foil rolling. The assumption that the roll remains convex is relaxed so that the strip profile may become concave, or thicken in the roll gap. However, we conjecture that the concave profile is associated with phenomena which occur after the rolls have stopped. We argue that the yield criterion must be satisfied in a nonconventional manner if such a phenomenon is caused plastically. Finite element analysis on an extrusion problem appears to confirm this conjecture.

Lateral bone density variations in the scoliotic spine

Adolescent Idiopathic Scoliosis (AIS) is the most common deformity of the spine, affecting 2-4% of the population. Previous studies have shown that the vertebrae in scoliotic spines undergo abnormal shape changes, however there has been little exploration of how AIS affects bone density distribution within the vertebrae. Existing pre-operative CT scans of 53 female idiopathic scoliosis patients with right-sided main thoracic curves were used to measure the lateral (right to left) bone density profile at mid-height through each vertebral body. This study demonstrated that AIS patients have a marked convex/concave asymmetry in bone density for vertebral levels at or near the apex of the scoliotic curve. To the best of our knowledge, the only previous studies of bone density distribution in AIS are those of Périé et al [1,2], who reported a coronal plane ‘mechanical migration’ of 0.54mm toward the concavity of the scoliotic curve in the lumbar apical vertebrae of 11 scoliosis patients. This is comparable to the value of 0.8mm (4%) in our study, especially since our patients had more severe scoliotic curves. From a bone adaptation perspective, these results suggest that the axial loading on the scoliotic spine is strongly asymmetric.

Lateral bone density variations in the scoliotic spine

Adolescent Idiopathic Scoliosis (AIS) is the most common deformity of the spine, affecting 2-4% of the population. Previous studies have shown that the vertebrae in scoliotic spines undergo abnormal shape changes, however there has been little exploration of how scoliosis affects bone density distribution within the vertebrae. In this study, existing CT scans of 53 female idiopathic scoliosis patients with right-sided main thoracic curves were used to measure the lateral (right to left) bone density profile at mid-height through each vertebral body. Five key bone density profile measures were identified from each normalised bone density distribution, and multiple regression analysis was performed to explore the relationship between bone density distribution and patient demographics (age, height, weight, body mass index (BMI), skeletal maturity, time since Menarche, vertebral level, and scoliosis curve severity). Results showed a marked convex/concave asymmetry in bone density for vertebral levels at or near the apex of the scoliotic curve. At the apical vertebra, mean bone density at the left side (concave) cortical shell was 23.5% higher than for the right (convex) cortical shell, and cancellous bone density along the central 60% of the lateral path from convex to concave increased by 13.8%. The centre of mass of the bone density profile at the thoracic curve apex was located 53.8% of the distance along the lateral path, indicating a shift of nearly 4% toward the concavity of the deformity. These lateral bone density gradients tapered off when moving away from the apical vertebra. Multi-linear regressions showed that the right cortical shell peak bone density is significantly correlated with skeletal maturity, with each Risser increment corresponding to an increase in mineral equivalent bone density of 4-5%. There were also statistically significant relationships between patient height, weight and BMI, and the gradient of cancellous bone density along the central 60% of the lateral path. Bone density gradient is positively correlated with weight, and negatively correlated with height and BMI, such that at the apical vertebra, a unit decrease in BMI corresponds to an almost 100% increase in bone density gradient.

New Approach on Robust Delay-Dependent H∞ Control for Uncertain T-S Fuzzy Systems With Interval Time-Varying Delay

This paper investigates the robust H∞ control for Takagi-Sugeno (T-S) fuzzy systems with interval time-varying delay. By employing a new and tighter integral inequality and constructing an appropriate type of Lyapunov functional, delay-dependent stability criteria are derived for the control problem. Because neither any model transformation nor free weighting matrices are employed in our theoretical derivation, the developed stability criteria significantly improve and simplify the existing stability conditions. Also, the maximum allowable upper delay bound and controller feedback gains can be obtained simultaneously from the developed approach by solving a constrained convex optimization problem. Numerical examples are given to demonstrate the effectiveness of the proposed methods.

Secondary curve behaviour in Lenke IC class adolescent idiopathic scoliosis following video assisted thoracoscopic spinal fusion

Introduction. Ideally after selective thoracic fusion for Lenke Class IC (i.e. major thoracic / secondary lumbar) curves, the lumbar spine will spontaneously accommodate to the corrected position of the thoracic curve, thereby achieving a balanced spine, avoiding the need for fusion of lumbar spinal segments1. The purpose of this study was to evaluate the behaviour of the lumbar curve in Lenke IC class adolescent idiopathic scoliosis (AIS) following video-assisted thoracoscopic spinal fusion and instrumentation (VATS) of the major thoracic curve. Methods. A retrospective review of 22 consecutive patients with AIS who underwent VATS by a single surgeon was conducted. The results were compared to published literature examining the behaviour of the secondary lumbar curve where other surgical approaches were employed. Results. Twenty-two patients (all female) with AIS underwent VATS. All major thoracic curves were right convex. The average age at surgery was 14 years (range 10 to 22 years). On average 6.7 levels (6 to 8) were instrumented. The mean follow-up was 25.1 months (6 to 36). The pre-operative major thoracic Cobb angle mean was 53.8° (40° to 75°). The pre-operative secondary lumbar Cobb angle mean was 43.9° (34° to 55°). On bending radiographs, the secondary curve corrected to 11.3° (0° to 35°). The rib hump mean measurement was 15.0° (7° to 21°). At latest follow-up the major thoracic Cobb angle measured on average 27.2° (20° to 41°) (p<0.001 – univariate ANOVA) and the mean secondary lumbar curve was 27.3° (15° to 42°) (p<0.001). This represented an uninstrumented secondary curve correction factor of 37.8%. The mean rib hump measured was 6.5° (2° to 15°) (p<0.001). The results above were comparable to published series when open surgery was performed. Discussion. VATS is an effective method of correcting major thoracic curves with secondary lumbar curves. The behaviour of the secondary lumbar curve is consistent with published series when open surgery, both anterior and posterior, is performed.

Design Optimisation of UAVs Systems achieved on a Framework Environment via Evolution and Game Theory

Over recent years, Unmanned Air Vehicles or UAVs have become a powerful tool for reconnaissance and surveillance tasks. These vehicles are now available in a broad size and capability range and are intended to fly in regions where the presence of onboard human pilots is either too risky or unnecessary. This paper describes the formulation and application of a design framework that supports the complex task of multidisciplinary design optimisation of UAVs systems via evolutionary computation. The framework includes a Graphical User Interface (GUI), a robust Evolutionary Algorithm optimiser named HAPEA, several design modules, mesh generators and post-processing capabilities in an integrated platform. These population –based algorithms such as EAs are good for cases problems where the search space can be multi-modal, non-convex or discontinuous, with multiple local minima and with noise, and also problems where we look for multiple solutions via Game Theory, namely a Nash equilibrium point or a Pareto set of non-dominated solutions. The application of the methodology is illustrated on conceptual and detailed multi-criteria and multidisciplinary shape design problems. Results indicate the practicality and robustness of the framework to find optimal shapes and trade—offs between the disciplinary analyses and to produce a set of non dominated solutions of an optimal Pareto front to the designer.

Iron burning in pressurised oxygen under microgravity conditions

An investigation of cylindrical iron rods burning in pressurised oxygen under microgravity conditions is presented. It has been shown that, under similar experimental conditions, the melting rate of a burning, cylindrical iron rod is higher in microgravity than in normal gravity by a factor of 1.8 ± 0.3. This paper presents microanalysis of quenched samples obtained in a microgravity environment in a 2.0 s duration drop tower facility in Brisbane, Australia. These images indicate that the solid/liquid interface is highly convex in reduced gravity, compared to the planar geometry typically observed in normal gravity, which increases the contact area between liquid and solid phases by a factor of 1.7 ± 0.1. Thus, there is good agreement between the proportional increase in solid/liquid interface surface area and melting rate in microgravity. This indicates that the cause of the increased melting rates for cylindrical iron rods burning in microgravity is altered interfacial geometry at the solid/liquid interface.