A note on a reaction-diffusion model describing the bone morphogen protein gradient in Drosophila embryonic patterning

In this article, we consider the Eldar model [3] from embryology in which a bone morphogenic protein, a short gastrulation protein, and their compound react and diffuse. We carry out a perturbation analysis in the limit of small diffusivity of the bone morphogenic protein. This analysis establishes conditions under which some elementary results of [3] are valid.

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.

Child health and the income gradient : evidence from Australia

The positive relationship between household income and child health is well documented in the child health literature but the precise mechanisms via which income generates better health and whether the income gradient is increasing in child age are not well understood. This paper presents new Australian evidence on the child health–income gradient. We use data from the Longitudinal Study of Australian Children (LSAC), which involved two waves of data collection for children born between March 2003 and February 2004 (B-Cohort: 0–3 years), and between March 1999 and February 2000 (K-Cohort: 4–7 years). This data set allows us to test the robustness of some of the findings of the influential studies of Case et al. [Case, A., Lubotsky, D., Paxson, C., 2002. Economic status and health in childhood: the origins of the gradient. The American Economic Review 92 (5) 1308–1344] and Currie and Stabile [Currie, J., Stabile, M., 2003. Socioeconomic status and child health: why is the relationship stronger for older children. The American Economic Review 93 (5) 1813–1823], and a recent study by Currie et al. [Currie, A., Shields, M.A., Price, S.W., 2007. The child health/family income gradient: evidence from England. Journal of Health Economics 26 (2) 213–232]. The richness of the LSAC data set also allows us to conduct further exploration of the determinants of child health. Our results reveal an increasing income gradient by child age using similar covariates to Case et al. [Case, A., Lubotsky, D., Paxson, C., 2002. Economic status and health in childhood: the origins of the gradient. The American Economic Review 92 (5) 1308–1344]. However, the income gradient disappears if we include a rich set of controls. Our results indicate that parental health and, in particular, the mother's health plays a significant role, reducing the income coefficient to zero; suggesting an underlying mechanism that can explain the observed relationship between child health and family income. Overall, our results for Australian children are similar to those produced by Propper et al. [Propper, C., Rigg, J., Burgess, S., 2007. Child health: evidence on the roles of family income and maternal mental health from a UK birth cohort. Health Economics 16 (11) 1245–1269] on their British child cohort.

What roles do contemporaneous and cumulative incomes play in the income–child health gradient for young children? Evidence from an Australian Panel

The literature to date shows that children from poorer households tend to have worse health than their peers, and the gap between them grows with age. We investigate whether and how health shocks (as measured by the onset of chronic conditions) contribute to the income–child health gradient and whether the contemporaneous or cumulative effects of income play important mitigating roles. We exploit a rich panel dataset with three panel waves called the Longitudinal Study of Australian children. Given the availability of three waves of data, we are able to apply a range of econometric techniques (e.g. fixed and random effects) to control for unobserved heterogeneity. The paper makes several contributions to the extant literature. First, it shows that an apparent income gradient becomes relatively attenuated in our dataset when the cumulative and contemporaneous effects of household income are distinguished econometrically. Second, it demonstrates that the income–child health gradient becomes statistically insignificant when controlling for parental health and health-related behaviours or unobserved heterogeneity.

Left ventricular volume and valve gradient analysis using an Apple Macintosh computer

A description of a computer program to analyse cine angiograms of the heart and pressure waveforms to calculate valve gradients.

The mechanical triggers of plaque rupture: Shear stress vs pressure gradient

The aim of this study was to evaluate the mechanical triggers that may cause plaque rupture. Wall shear stress (WSS) and pressure gradient are the direct mechanical forces acting on the plaque in a stenotic artery. Their influence on plaque stability is thought to be controversial. This study used a physiologically realistic, pulsatile flow, two-dimensional, cine phase-contrast MRI sequence in a patient with a 70% carotid stenosis. Instead of considering the full patient-specific carotid bifurcation derived from MRI, only the plaque region has been modelled by means of the idealised flow model. WSS reached a local maximum just distal to the stenosis followed by a negative local minimum. A pressure drop across the stenosis was found which varied significantly during systole and diastole. The ratio of the relative importance of WSS and pressure was assessed and was found to be less than 0.07% for all time phases, even at the throat of the stenosis. In conclusion, although the local high WSS at the stenosis may damage the endothelium and fissure plaque, the magnitude of WSS is small compared with the overall loading on plaque. Therefore, pressure may be the main mechanical trigger for plaque rupture and risk stratification using stress analysis of plaque stability may only need to consider the pressure effect.

Development of a transient gradient enhanced non local continuum damage mechanics model for masonry

Due to the advent of varied types of masonry systems a comprehensive failure mechanism of masonry essential for the understanding of its behaviour is impossible to be determined from experimental testing. As masonry is predominantly used in wall structures a biaxial stress state dominates its failure mechanism. Biaxial testing will therefore be necessary for each type of masonry, which is expensive and time consuming. A computational method would be advantageous; however masonry is complex to model which requires advanced computational modelling methods. This thesis has formulated a damage mechanics inspired modelling method and has shown that the method effectively determines the failure mechanisms and deformation characteristics of masonry under biaxial states of loading.

A second order control-volume finite-element least-squares strategy for simulating diffusion in strongly anisotropic media

An unstructured mesh �nite volume discretisation method for simulating di�usion in anisotropic media in two-dimensional space is discussed. This technique is considered as an extension of the fully implicit hybrid control-volume �nite-element method and it retains the local continuity of the ux at the control volume faces. A least squares function recon- struction technique together with a new ux decomposition strategy is used to obtain an accurate ux approximation at the control volume face, ensuring that the overall accuracy of the spatial discretisation maintains second order. This paper highlights that the new technique coincides with the traditional shape function technique when the correction term is neglected and that it signi�cantly increases the accuracy of the previous linear scheme on coarse meshes when applied to media that exhibit very strong to extreme anisotropy ratios. It is concluded that the method can be used on both regular and irregular meshes, and appears independent of the mesh quality.

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.

Age-related development of a refractive index plateau in the human lens : evidence for a distinct nucleus

The human lens comprises two distinct regions in which the refractive index changes at different rates. The periphery contains a rapidly increasing refractive index gradient, which becomes steeper with age. The inner region contains a shallow gradient, which flattens with age, due to formation of a central plateau, of RI = 1.418, which reaches a maximum size of 7.0 × 3.05 mm around age 60 years. Formation of the plateau can be attributed to compression of fibre cells generated in prenatal life. Present in prenatal but not in postnatal fibre cells, γ-crystallin may play a role in limiting nuclear cell compression.

Robot navigation in sensor space

This thesis investigates the problem of robot navigation using only landmark bearings. The proposed system allows a robot to move to a ground target location specified by the sensor values observed at this ground target posi- tion. The control actions are computed based on the difference between the current landmark bearings and the target landmark bearings. No Cartesian coordinates with respect to the ground are computed by the control system. The robot navigates using solely information from the bearing sensor space. Most existing robot navigation systems require a ground frame (2D Cartesian coordinate system) in order to navigate from a ground point A to a ground point B. The commonly used sensors such as laser range scanner, sonar, infrared, and vision do not directly provide the 2D ground coordi- nates of the robot. The existing systems use the sensor measurements to localise the robot with respect to a map, a set of 2D coordinates of the objects of interest. It is more natural to navigate between the points in the sensor space corresponding to A and B without requiring the Cartesian map and the localisation process. Research on animals has revealed how insects are able to exploit very limited computational and memory resources to successfully navigate to a desired destination without computing Cartesian positions. For example, a honeybee balances the left and right optical flows to navigate in a nar- row corridor. Unlike many other ants, Cataglyphis bicolor does not secrete pheromone trails in order to find its way home but instead uses the sun as a compass to keep track of its home direction vector. The home vector can be inaccurate, so the ant also uses landmark recognition. More precisely, it takes snapshots and compass headings of some landmarks. To return home, the ant tries to line up the landmarks exactly as they were before it started wandering. This thesis introduces a navigation method based on reflex actions in sensor space. The sensor vector is made of the bearings of some landmarks, and the reflex action is a gradient descent with respect to the distance in sensor space between the current sensor vector and the target sensor vec- tor. Our theoretical analysis shows that except for some fully characterized pathological cases, any point is reachable from any other point by reflex action in the bearing sensor space provided the environment contains three landmarks and is free of obstacles. The trajectories of a robot using reflex navigation, like other image- based visual control strategies, do not correspond necessarily to the shortest paths on the ground, because the sensor error is minimized, not the moving distance on the ground. However, we show that the use of a sequence of waypoints in sensor space can address this problem. In order to identify relevant waypoints, we train a Self Organising Map (SOM) from a set of observations uniformly distributed with respect to the ground. This SOM provides a sense of location to the robot, and allows a form of path planning in sensor space. The navigation proposed system is analysed theoretically, and evaluated both in simulation and with experiments on a real robot.

Decision support system for contractor pre-qualification : artificial neural network model

The selection criteria for contractor pre-qualification are characterized by the co-existence of both quantitative and qualitative data. The qualitative data is non-linear, uncertain and imprecise. An ideal decision support system for contractor pre-qualification should have the ability of handling both quantitative and qualitative data, and of mapping the complicated nonlinear relationship of the selection criteria, such that rational and consistent decisions can be made. In this research paper, an artificial neural network model was developed to assist public clients identifying suitable contractors for tendering. The pre-qualification criteria (variables) were identified for the model. One hundred and twelve real pre-qualification cases were collected from civil engineering projects in Hong Kong, and eighty-eight hypothetical pre-qualification cases were also generated according to the “If-then” rules used by professionals in the pre-qualification process. The results of the analysis totally comply with current practice (public developers in Hong Kong). Each pre-qualification case consisted of input ratings for candidate contractors’ attributes and their corresponding pre-qualification decisions. The training of the neural network model was accomplished by using the developed program, in which a conjugate gradient descent algorithm was incorporated for improving the learning performance of the network. Cross-validation was applied to estimate the generalization errors based on the “re-sampling” of training pairs. The case studies show that the artificial neural network model is suitable for mapping the complicated nonlinear relationship between contractors’ attributes and their corresponding pre-qualification (disqualification) decisions. The artificial neural network model can be concluded as an ideal alternative for performing the contractor pre-qualification task.

Improved GrabCut segmentation via GMM optimisation

Semi-automatic segmentation of still images has vast and varied practical applications. Recently, an approach "GrabCut" has managed to successfully build upon earlier approaches based on colour and gradient information in order to address the problem of efficient extraction of a foreground object in a complex environment. In this paper, we extend the GrabCut algorithm further by applying an unsupervised algorithm for modelling the Gaussian Mixtures that are used to define the foreground and background in the segmentation algorithm. We show examples where the optimisation of the GrabCut framework leads to further improvements in performance.