Trajectory characterizations for a discrete-time bearing-only navigation strategy

In this paper we explore the geometry of a particular navigation scheme which guides a pursuer from a fixed initial position to a given fixed final position using a one-step look ahead strategy and using only bearing measurements. We explicitly characterize the optimal trajectories for the problem in terms of the Cramer-Rao bound such that the derived trajectories permit a minimization in the error of an unbiased estimate of the target position.

Reduced-order output feedback controllers for discrete-time systems

This article considers the stabilization by output feedback controllers for discrete-time systems. The controller can place all of the closed-loop poles within a specified disk D(-α, 1/β), centred at (-α,0) with radius 1/β, where | - α|  + 1/β < 1. The design method involves the decomposition of the system into two portions. The first portion comprises of all of the poles that are lying outside of the specified disk. A reduced-order model is constructed for this portion. The second portion comprises of all of the remaining poles of the system and is characterized by an H_∞-norm bound. The controller design is then accomplished by using H_∞-control theory. It is shown that, subject to the solvability of an algebraic Riccati equation, output feedback controllers can be systematically derived. The order of the controller is low, and can be as low as the number of the open-loop poles that are lying outside of the specified disk. A step-by-step design algorithm is provided. Numerical examples are given to illustrate the attractiveness of the design method.

Using fractal geometry to make rapid field measurements of riverbed topography at ecologically useful spatial scales

A method is described for making rapid in situ field measurements of riverbed topography over spatial scales of ≅1–10 m. This method uses rolling balls to make quick, accurate measurements of river-bed roughness at several spatial scales. Random sampling and replication generate multiple estimates of the fractal dimension (d) that can be used to test for significant differences in the complexity of riverbed architecture between habitat types and spatial scales.

Objective classification of fabric pilling based on the two-dimensional discrete wavelet transform

A number of methods for automated objective ratings of fabric pilling based on image analysis are described in the literature. The periodic structure of fabrics makes them suitable candidates for frequency domain analysis. We propose a new method of frequency domain analysis based on the two-dimensional discrete wavelet transform to objectively measure pilling intensity in sample images. We present a preliminary evaluation of the proposed method based on analysis of two series of standard pilling evaluation test images. The initial results suggest that the proposed method is feasible, and that the ability of the method to discriminate between levels of pilling intensity depends on the wavelet analysis scale being closely matched to the fabric interyarn pitch. We also present a heuristic method for optimal selection of an analysis wavelet and associated analysis scale.

Geometry and combinatorics of the cutting angle method

Lower approximation of Lipschitz functions plays an important role in deterministic global optimization. This article examines in detail the lower piecewise linear approximation which arises in the cutting angle method. All its local minima can be explicitly enumerated, and a special data structure was designed to process them very efficiently, improving previous results by several orders of magnitude. Further, some geometrical properties of the lower approximation have been studied, and regions on which this function is linear have been identified explicitly. Connection to a special distance function and Voronoi diagrams was established. An application of these results is a black-box multivariate random number generator, based on acceptance-rejection approach.

Application of a discrete event simulation for robust system design of a melt facility

This paper presents a methodology to identify robust operating regions through the selection of controllable factory variables, using discrete event simulation. A casting plant melt facility was used as an industrial test bed to develop these techniques. A robust system design was determined by response surface analysis of key production parameters. Furthermore, robust operating policies that maximise throughput, while minimizing work-in-progress and thus energy consumption were identified.

The relationship between muscle size and bone geometry during growth and in response to exercise

As muscles become larger and stronger during growth and in response to increased loading, bones should adapt by adding mass, size, and strength. In this unilateral model, we tested the hypothesis that (1) the relationship between muscle size and bone mass and geometry (nonplaying arm) would not change during different stages of puberty and (2) exercise would not alter the relationship between muscle and bone, that is, additional loading would result in a similar unit increment in both muscle and bone mass, bone size, and bending strength during growth. We studied 47 competitive female tennis players aged 8–17 years. Total, cortical, and medullary cross-sectional areas, muscle area, and the polar second moment of area (Ip) were calculated in the playing and nonplaying arms using magnetic resonance imaging (MRI); BMC was assessed by DXA. Growth effects: In the nonplaying arm in pre-, peri- and post-pubertal players, muscle area was linearly associated BMC, total and cortical area, and Ip (r = 0.56–0.81, P < 0.09 to < 0.001), independent of age. No detectable differences were found between pubertal groups for the slope of the relationship between muscle and bone traits. Post-pubertal players, however, had a higher BMC and cortical area relative to muscle area (i.e., higher intercept) than pre- and peri-pubertal players (P < 0.05 to < 0.01), independent of age; pre- and peri-pubertal players had a greater medullary area relative to muscle area than post-pubertal players (P < 0.05 to < 0.01). Exercise effects: Comparison of the side-to-side differences revealed that muscle and bone traits were 6–13% greater in the playing arm in pre-pubertal players, and did not increase with advancing maturation. In all players, the percent (and absolute) side-to-side differences in muscle area were positively correlated with the percent (and absolute) differences in BMC, total and cortical area, and Ip (r = 0.36–0.40, P < 0.05 to < 0.001). However, the side-to-side differences in muscle area only accounted for 11.8–15.9% of the variance of the differences in bone mass, bone size, and bending strength. This suggests that other factors associated with loading distinct from muscle size itself contributed to the bones adaptive response during growth. Therefore, the unifying hypothesis that larger muscles induced by exercise led to a proportional increase in bone mass, bone size, and bending strength appears to be simplistic and denies the influence of other factors in the development of bone mass and bone shape.

Evaluating the robustness of objective pilling classification with the two-dimensional discrete wavelet transform

Previously, we proposed a new method of frequency domain analysis based on the two-dimensional discrete wavelet transform to objectively measure pilling intensity in sample fabric images. We have further evaluated this method, and our results indicate that it is robust to small horizontal and/or vertical translations and to significant variations in the brightness of the image under analysis, and is sensitive to rotation and to dilation of the image. These results suggest that as long as precautions are taken to ensure fabric test samples are imaged under consistent conditions of weave/knit pattern alignment (rotation) and apparent interyarn pitch (dilation), the method will yield repeatable results.

Influence of the geometry of an immersed steel workpiece on mass transfer coefficient in a chemical heat treatment fluidised bed

The mass transfer during carburising in a fluidised bed and in a steel workpiece has been studied experimentally in this work. This involved carburising experiment in an electrically heated fluidised bed at 900–970°C with natural gas and air as the atmosphere. A steel workpiece was designed to provide a range of carbon transfer surfaces of different geometries in the fluidised bed, and the carbon transfer coefficient was measured at these surfaces. The carbon transfer coefficient was determined from the carbon distribution within the diffusion layer of the sample. An empirical relationship of the carbon potential as a function of carburising atmosphere, bed temperature and fluidising velocity was determined, based on the understanding of the mass transfer mechanism and analysis of the experimental results.

A computational approach to the reconstruction of surface geometry from early temple superstructures

Recovering the control or implicit geometry underlying temple architecture requires bringing together fragments of evidence from field measurements, relating these to mathematical and geometric descriptions in canonical texts and proposing "best-fit" constructive models. While scholars in the field have traditionally used manual methods, the innovative application of niche computational techniques can help extend the study of artefact geometry. This paper demonstrates the application of a hybrid computational approach to the problem of recovering the surface geometry of early temple superstructures. The approach combines field measurements of temples, close-range architectural photogrammetry, rule-based generation and parametric modelling. The computing of surface geometry comprises a rule-based global model governing the overall form of the superstructure, several local models for individual motifs using photogrammetry and an intermediate geometry model that combines the two. To explain the technique and the different models, the paper examines an illustrative example of surface geometry reconstruction based on studies undertaken on a tenth century stone superstructure from western India. The example demonstrates that a combination of computational methods yields sophisticated models of the constructive geometry underlying temple form and that these digital artefacts can form the basis for in depth comparative analysis of temples, arising out of similar techniques, spread over geography, culture and time.

Long-term effects of calcium-vitamin-D3-fortified milk on bone geometry and strength in older men

The long-term effects of calcium and vitamin D supplementation on bone material and structural properties in older men are not known. The aim of this study was to examine the effects of high calcium (1000 mg/day)- and vitamin-D3 (800 IU/day)-fortified milk on cortical and trabecular volumetric BMD (vBMD) and bone geometry at the axial and appendicular skeleton in men aged over 50 years. One hundred and eleven men who were part of a larger 2-year randomized controlled trial had QCT scans of the mid-femur and lumbar spine (L1–L3) to assess vBMD, bone geometry and indices of bone strength [polar moment of inertia (Ipolar)]. After 2 years, there were no significant differences between the milk supplementation and control group for the change in any mid-femur or L1–L3 bone parameters for all men aged over 50 years. However, the mid-femur skeletal responses to the fortified milk varied according to age, with a split of ≤62 versus >62 years being the most significant for discriminating the changes between the two groups. Subsequent analysis revealed that, in the older men (>62 years), the expansion in mid-femur medullary area was 2.8% (P < 0.01) less in the milk supplementation compared to control group, which helped to preserve cortical area in the milk supplementation group (between group difference 1.1%, P < 0.01). Similarly, for mid-femur cortical vBMD and Ipolar, the net loss was 2.3 and 2.8% less in the milk supplementation compared to control group (P < 0.01 and <0.001, respectively). In conclusion, calcium–vitamin-D3-fortified milk may represent an effective strategy to maintain bone strength by preventing endocortical bone loss and slowing the loss in cortical vBMD in elderly men.

Parallelization of the discrete gradient method of non-smooth optimization and its applications

We investigate parallelization and performance of the discrete gradient method of nonsmooth optimization. This derivative free method is shown to be an effective optimization tool, able to skip many shallow local minima of nonconvex nondifferentiable objective functions. Although this is a sequential iterative method, we were able to parallelize critical steps of the algorithm, and this lead to a significant improvement in performance on multiprocessor computer clusters. We applied this method to a difficult polyatomic clusters problem in computational chemistry, and found this method to outperform other algorithms.

Predicting the distribution of discrete spatial events using artificial neural networks

Although the development of geographic information system (GIS) technology and digital data manipulation techniques has enabled practitioners in the geographical and geophysical sciences to make more efficient use of resource information, many of the methods used in forming spatial prediction models are still inherently based on traditional techniques of map stacking in which layers of data are combined under the guidance of a theoretical domain model. This paper describes a data-driven approach by which Artificial Neural Networks (ANNs) can be trained to represent a function characterising the probability that an instance of a discrete event, such as the presence of a mineral deposit or the sighting of an endangered animal species, will occur over some grid element of the spatial area under consideration. A case study describes the application of the technique to the task of mineral prospectivity mapping in the Castlemaine region of Victoria using a range of geological, geophysical and geochemical input variables. Comparison of the maps produced using neural networks with maps produced using a density estimation-based technique demonstrates that the maps can reliably be interpreted as representing probabilities. However, while the neural network model and the density estimation-based model yield similar results under an appropriate choice of values for the respective parameters, the neural network approach has several advantages, especially in high dimensional input spaces.