Some Remarks on the Approximation of Transitional Density in Stochastic Differential Equations

Aijt-Sahalia (2002) introduced a method to estimate transitional probability densities of di®usion processes by means of Hermite expansions with coe±cients determined by means of Taylor series. This note describes a numerical procedure to ¯nd these coe±cients based on the calculation of moments. One advantage of this procedure is that it can be used e®ectively when the mathematical operations required to ¯nd closed-form expressions for these coe±cients are otherwise infeasible.

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.

Temporal construal in advertising : the moderating role of temporal orientation and attribute importance in consumer evaluations

In two experiments, we study how the temporal orientation of consumers (i.e., future-oriented or present-oriented), temporal construal (distant future, near future), and product attribute importance (primary, secondary) influence advertisement evaluations. Data suggest that future-oriented consumers react most favorably to ads that feature a product to be released in the distant future and that highlight primary product attributes. In contrast, present-oriented consumers prefer near-future ads that highlight secondary product attributes. Study 2 shows that consumer attitudes are mediated by perceptions of attribute diagnosticity (i.e., the perceived usefulness of the attribute information). Together, these experiments shed light on how individual differences, such as temporal orientation, offer valuable insights into temporal construal effects in advertising.

The role of land use and psycho-social factors in high density residents' work travel mode choices : implications for sustainable transport policy

Imperatives to improve the sustainability of cities often hinge upon plans to increase urban residential density to facilitate greater reliance on sustainable forms of transport and minimise car use. However there is ongoing debate about whether high residential density land use in isolation results in sustainable transport outcomes. Findings from surveys with residents of inner-urban high density dwellings in Brisbane, Australia, suggest that solo car travel accounts for the greatest modal share of typical work journeys and attitudes toward dwelling and neighbourhood transport-related features, residential sorting factors and socio-demographics, alongside land use such as public transport availability, are significantly associated with work travel mode choice. We discuss the implications of our findings for transport policy and management including encouraging relatively sustainable intermodal forms of transport for work journeys.

Sensitivity of proximal femoral stiffness and areal bone mineral density to changes in bone geometry and density

Areal bone mineral density (aBMD) is the most common surrogate measurement for assessing the bone strength of the proximal femur associated with osteoporosis. Additional factors, however, contribute to the overall strength of the proximal femur, primarily the anatomical geometry. Finite element analysis (FEA) is an effective and widely used computerbased simulation technique for modeling mechanical loading of various engineering structures, providing predictions of displacement and induced stress distribution due to the applied load. FEA is therefore inherently dependent upon both density and anatomical geometry. FEA may be performed on both three-dimensional and two-dimensional models of the proximal femur derived from radiographic images, from which the mechanical stiffness may be redicted. It is examined whether the outcome measures of two-dimensional FEA, two-dimensional, finite element analysis of X-ray images (FEXI), and three-dimensional FEA computed stiffness of the proximal femur were more sensitive than aBMD to changes in trabecular bone density and femur geometry. It is assumed that if an outcome measure follows known trends with changes in density and geometric parameters, then an increased sensitivity will be indicative of an improved prediction of bone strength. All three outcome measures increased non-linearly with trabecular bone density, increased linearly with cortical shell thickness and neck width, decreased linearly with neck length, and were relatively insensitive to neck-shaft angle. For femoral head radius, aBMD was relatively insensitive, with two-dimensional FEXI and threedimensional FEA demonstrating a non-linear increase and decrease in sensitivity, respectively. For neck anteversion, aBMD decreased non-linearly, whereas both two-dimensional FEXI and three dimensional FEA demonstrated a parabolic-type relationship, with maximum stiffness achieved at an angle of approximately 15o. Multi-parameter analysis showed that all three outcome measures demonstrated their highest sensitivity to a change in cortical thickness. When changes in all input parameters were considered simultaneously, three and twodimensional FEA had statistically equal sensitivities (0.41±0.20 and 0.42±0.16 respectively, p = ns) that were significantly higher than the sensitivity of aBMD (0.24±0.07; p = 0.014 and 0.002 for three-dimensional and two-dimensional FEA respectively). This simulation study suggests that since mechanical integrity and FEA are inherently dependent upon anatomical geometry, FEXI stiffness, being derived from conventional two-dimensional radiographic images, may provide an improvement in the prediction of bone strength of the proximal femur than currently provided by aBMD.

A 1H-MRS investigation of the medial temporal lobe in antipsychotic-naïve and early-treated first episode psychosis

Schizophrenia is associated with significant brain abnormalities, including changes in brain metabolites as measured by proton magnetic resonance spectroscopy (MRS). What remains unclear is the extent to which these changes are a consequence of the emergence of psychotic disorders or the result of treatment with antipsychotic medication. We assessed 34 patients with first episode psychosis (15 antipsychotic naïve) and 19 age- and gender-matched controls using short-echo MRS in the medial temporal lobe bilaterally. Overall, there were no differences in any metabolite, regardless of treatment status. However, when the analysis was limited to patients with a diagnosis of schizophrenia, schizophreniform or schizoaffective disorder, significant elevations of creatine/phosphocreatine (Cr/PCr) and myo-inositol (mI) were found in the treated group. These data indicate a relative absence of temporal lobe metabolic abnormalities in first episode psychosis, but suggest that some treatment-related changes in mI might be apparent in patients with schizophrenia-spectrum diagnoses. Seemingly illness-related Cr/PCr elevations were also specific to the diagnosis of schizophrenia-spectrum disorder and seem worthy of future study.

Corneal sensitivity and slit scanning in vivo confocal microscopy of the subbasal nerve plexus of the normal central and peripheral human cornea

Purpose: To determine the subbasal nerve density and tortuosity at 5 corneal locations and to investigate whether these microstructural observations correlate with corneal sensitivity. Method: Sixty eyes of 60 normal human subjects were recruited into 1 of 3 age groups, group 1: aged ,35 years, group 2: aged 35–50 years, and group 3: aged .50 years. All eyes were examined using slit-lamp biomicroscopy, noncontact corneal esthesiometry, and slit scanning in vivo confocal microscopy. Results: The mean subbasal nerve density and the mean corneal sensitivity were greatest centrally (14,731 6 6056 mm/mm2 and 0.38 6 0.21 millibars, respectively) and lowest in the nasal mid periphery (7850 6 4947 mm/mm2 and 0.49 6 0.25 millibars, respectively). The mean subbasal nerve tortuosity coefficient was greatest in the temporal mid periphery (27.3 6 6.4) and lowest in the superior mid periphery (19.3 6 14.1). There was no significant difference in mean total subbasal nerve density between age groups. However, corneal sensation (P = 0.001) and subbasal nerve tortuosity (P = 0.004) demonstrated significant differences between age groups. Subbasal nerve density only showed significant correlations with corneal sensitivity threshold in the temporal cornea and with subbasal nerve tortuosity in the inferior and nasal cornea. However, these correlations were weak. Conclusions: This study quantitatively analyzes living human corneal nerve structure and an aspect of nerve function. There is no strong correlation between subbasal nerve density and corneal sensation. This study provides useful baseline data for the normal living human cornea at central and mid-peripheral locations

Strategic short termism as an issue of top-teams’ temporal orientation

Short-termism among firms, the tendency to excessively discount long-term benefits and favour less valuable short-term benefits, has been a prominent issue in business and public policy debates but research to date has been inconclusive. We study how managers frame, interpret, and resolve problems of intertemporal choice in actual decisions by using computer aided text analysis to measure the frequency of top-team temporal references in 1653 listed Australian firms between 1992-2005. Contrary to short-termism arguments we find evidence of a significant general increase in Future orientation and a significant decrease in Current/Past orientation. We also show top-teams’ temporal orientation is related to their strategic orientation, specifically the extent to which they focus on Innovation-Expansion and Capacity Building.

Functional outcome of transfemoral amputees fitted with an osseointegrated fixation : temporal gait characteristics

The purpose of this study was to characterise the functional outcome of 12 transfemoral amputees fitted with osseointegrated fixation using temporal gait characteristics. The objectives were (A) to present the cadence, duration of gait cycle, support and swing phases with an emphasis on the stride-to-stride and participant-to-participant variability, and (B) to compare these temporal variables with normative data extracted from the literature focusing on transfemoral amputees fitted with a socket and able-bodied participants. The temporal variables were extracted from the load applied on the residuum during straight level walking, which was collected at 200 Hz by a transducer. A total of 613 strides were assessed. The cadence (46±4 strides/min), the duration of the gait cycle (1.29±0.11 s), support (0.73±0.07 s, 57±3% of CG) and swing (0.56±0.07 s, 43±3% of GC) phases of the participants were 2% quicker, 3%, 6% shorter and 1% longer than transfemoral amputees using a socket as well as 11% slower, 9%, 6% and 13% longer than able-bodied, respectively. All combined, the results indicated that the fitting of an osseointegrated fixation has enabled this group of amputees to restore their locomotion with a highly functional level. Further longitudinal and cross-sectional studies would be required to confirm these outcomes. Nonetheless, the data presented can be used as benchmark for future comparisons. It can also be used as input in generic algorithms using templates of patterns of loading to recognise activities of daily living and to detect falls.

Addressing issues in sparseness, ecological bias and formulation of the adjacency matrix in Bayesian spatio-temporal analysis of disease counts

The main objective of this PhD was to further develop Bayesian spatio-temporal models (specifically the Conditional Autoregressive (CAR) class of models), for the analysis of sparse disease outcomes such as birth defects. The motivation for the thesis arose from problems encountered when analyzing a large birth defect registry in New South Wales. The specific components and related research objectives of the thesis were developed from gaps in the literature on current formulations of the CAR model, and health service planning requirements. Data from a large probabilistically-linked database from 1990 to 2004, consisting of fields from two separate registries: the Birth Defect Registry (BDR) and Midwives Data Collection (MDC) were used in the analyses in this thesis. The main objective was split into smaller goals. The first goal was to determine how the specification of the neighbourhood weight matrix will affect the smoothing properties of the CAR model, and this is the focus of chapter 6. Secondly, I hoped to evaluate the usefulness of incorporating a zero-inflated Poisson (ZIP) component as well as a shared-component model in terms of modeling a sparse outcome, and this is carried out in chapter 7. The third goal was to identify optimal sampling and sample size schemes designed to select individual level data for a hybrid ecological spatial model, and this is done in chapter 8. Finally, I wanted to put together the earlier improvements to the CAR model, and along with demographic projections, provide forecasts for birth defects at the SLA level. Chapter 9 describes how this is done. For the first objective, I examined a series of neighbourhood weight matrices, and showed how smoothing the relative risk estimates according to similarity by an important covariate (i.e. maternal age) helped improve the model’s ability to recover the underlying risk, as compared to the traditional adjacency (specifically the Queen) method of applying weights. Next, to address the sparseness and excess zeros commonly encountered in the analysis of rare outcomes such as birth defects, I compared a few models, including an extension of the usual Poisson model to encompass excess zeros in the data. This was achieved via a mixture model, which also encompassed the shared component model to improve on the estimation of sparse counts through borrowing strength across a shared component (e.g. latent risk factor/s) with the referent outcome (caesarean section was used in this example). Using the Deviance Information Criteria (DIC), I showed how the proposed model performed better than the usual models, but only when both outcomes shared a strong spatial correlation. The next objective involved identifying the optimal sampling and sample size strategy for incorporating individual-level data with areal covariates in a hybrid study design. I performed extensive simulation studies, evaluating thirteen different sampling schemes along with variations in sample size. This was done in the context of an ecological regression model that incorporated spatial correlation in the outcomes, as well as accommodating both individual and areal measures of covariates. Using the Average Mean Squared Error (AMSE), I showed how a simple random sample of 20% of the SLAs, followed by selecting all cases in the SLAs chosen, along with an equal number of controls, provided the lowest AMSE. The final objective involved combining the improved spatio-temporal CAR model with population (i.e. women) forecasts, to provide 30-year annual estimates of birth defects at the Statistical Local Area (SLA) level in New South Wales, Australia. The projections were illustrated using sixteen different SLAs, representing the various areal measures of socio-economic status and remoteness. A sensitivity analysis of the assumptions used in the projection was also undertaken. By the end of the thesis, I will show how challenges in the spatial analysis of rare diseases such as birth defects can be addressed, by specifically formulating the neighbourhood weight matrix to smooth according to a key covariate (i.e. maternal age), incorporating a ZIP component to model excess zeros in outcomes and borrowing strength from a referent outcome (i.e. caesarean counts). An efficient strategy to sample individual-level data and sample size considerations for rare disease will also be presented. Finally, projections in birth defect categories at the SLA level will be made.