Experimental evaluation of hotspot identification methods

Identifying crash “hotspots”, “blackspots”, “sites with promise”, or “high risk” locations is standard practice in departments of transportation throughout the US. The literature is replete with the development and discussion of statistical methods for hotspot identification (HSID). Theoretical derivations and empirical studies have been used to weigh the benefits of various HSID methods; however, a small number of studies have used controlled experiments to systematically assess various methods. Using experimentally derived simulated data—which are argued to be superior to empirical data, three hot spot identification methods observed in practice are evaluated: simple ranking, confidence interval, and Empirical Bayes. Using simulated data, sites with promise are known a priori, in contrast to empirical data where high risk sites are not known for certain. To conduct the evaluation, properties of observed crash data are used to generate simulated crash frequency distributions at hypothetical sites. A variety of factors is manipulated to simulate a host of ‘real world’ conditions. Various levels of confidence are explored, and false positives (identifying a safe site as high risk) and false negatives (identifying a high risk site as safe) are compared across methods. Finally, the effects of crash history duration in the three HSID approaches are assessed. The results illustrate that the Empirical Bayes technique significantly outperforms ranking and confidence interval techniques (with certain caveats). As found by others, false positives and negatives are inversely related. Three years of crash history appears, in general, to provide an appropriate crash history duration.

Socioeconomic inequality profiles in physical and developmental health from 0-7 years : Australian National Study

Background: Early and persistent exposure to socioeconomic disadvantage impairs children’s health and wellbeing. However, it is unclear at what age health inequalities emerge or whether these relationships vary across ages and outcomes. We address these issues using cross-sectional Australian population data on the physical and developmental health of children at ages 0-1, 2-3, 4-5 and 6-7 years. Methods: 10 physical and developmental health outcomes were assessed in 2004 and 2006 for two cohorts each comprising around 5000 children. Socioeconomic position was measured as a composite of parental education, occupation and household income. Results: Lower socioeconomic position was associated with increased odds for poor outcomes. For physical health outcomes and socio-emotional competence, associations were similar across age groups and were consistent with either threshold effects (for poor general health, special healthcare needs and socio-emotional competence) or gradient effects (for illness with wheeze, sleep problems and injury). For socio-emotional difficulties, communication, vocabulary and emergent literacy, stronger socioeconomic associations were observed. The patterns were linear or accelerated and varied across ages. Conclusions: From very early childhood, social disadvantage was associated with poorer outcomes across most measures of physical and developmental health and showed no evidence of either strengthening or attenuating at older compared to younger ages. Findings confirm the importance of early childhood as a key focus for health promotion and prevention efforts.

Wavelet based approaches and high resolution methods for complex process models

Many industrial processes and systems can be modelled mathematically by a set of Partial Differential Equations (PDEs). Finding a solution to such a PDF model is essential for system design, simulation, and process control purpose. However, major difficulties appear when solving PDEs with singularity. Traditional numerical methods, such as finite difference, finite element, and polynomial based orthogonal collocation, not only have limitations to fully capture the process dynamics but also demand enormous computation power due to the large number of elements or mesh points for accommodation of sharp variations. To tackle this challenging problem, wavelet based approaches and high resolution methods have been recently developed with successful applications to a fixedbed adsorption column model. Our investigation has shown that recent advances in wavelet based approaches and high resolution methods have the potential to be adopted for solving more complicated dynamic system models. This chapter will highlight the successful applications of these new methods in solving complex models of simulated-moving-bed (SMB) chromatographic processes. A SMB process is a distributed parameter system and can be mathematically described by a set of partial/ordinary differential equations and algebraic equations. These equations are highly coupled; experience wave propagations with steep front, and require significant numerical effort to solve. To demonstrate the numerical computing power of the wavelet based approaches and high resolution methods, a single column chromatographic process modelled by a Transport-Dispersive-Equilibrium linear model is investigated first. Numerical solutions from the upwind-1 finite difference, wavelet-collocation, and high resolution methods are evaluated by quantitative comparisons with the analytical solution for a range of Peclet numbers. After that, the advantages of the wavelet based approaches and high resolution methods are further demonstrated through applications to a dynamic SMB model for an enantiomers separation process. This research has revealed that for a PDE system with a low Peclet number, all existing numerical methods work well, but the upwind finite difference method consumes the most time for the same degree of accuracy of the numerical solution. The high resolution method provides an accurate numerical solution for a PDE system with a medium Peclet number. The wavelet collocation method is capable of catching up steep changes in the solution, and thus can be used for solving PDE models with high singularity. For the complex SMB system models under consideration, both the wavelet based approaches and high resolution methods are good candidates in terms of computation demand and prediction accuracy on the steep front. The high resolution methods have shown better stability in achieving steady state in the specific case studied in this Chapter.

Analysis of cardiac and epileptic signals using higher order spectra

The theory of nonlinear dyamic systems provides some new methods to handle complex systems. Chaos theory offers new concepts, algorithms and methods for processing, enhancing and analyzing the measured signals. In recent years, researchers are applying the concepts from this theory to bio-signal analysis. In this work, the complex dynamics of the bio-signals such as electrocardiogram (ECG) and electroencephalogram (EEG) are analyzed using the tools of nonlinear systems theory. In the modern industrialized countries every year several hundred thousands of people die due to sudden cardiac death. The Electrocardiogram (ECG) is an important biosignal representing the sum total of millions of cardiac cell depolarization potentials. It contains important insight into the state of health and nature of the disease afflicting the heart. Heart rate variability (HRV) refers to the regulation of the sinoatrial node, the natural pacemaker of the heart by the sympathetic and parasympathetic branches of the autonomic nervous system. Heart rate variability analysis is an important tool to observe the heart's ability to respond to normal regulatory impulses that affect its rhythm. A computerbased intelligent system for analysis of cardiac states is very useful in diagnostics and disease management. Like many bio-signals, HRV signals are non-linear in nature. Higher order spectral analysis (HOS) is known to be a good tool for the analysis of non-linear systems and provides good noise immunity. In this work, we studied the HOS of the HRV signals of normal heartbeat and four classes of arrhythmia. This thesis presents some general characteristics for each of these classes of HRV signals in the bispectrum and bicoherence plots. Several features were extracted from the HOS and subjected an Analysis of Variance (ANOVA) test. The results are very promising for cardiac arrhythmia classification with a number of features yielding a p-value < 0.02 in the ANOVA test. An automated intelligent system for the identification of cardiac health is very useful in healthcare technology. In this work, seven features were extracted from the heart rate signals using HOS and fed to a support vector machine (SVM) for classification. The performance evaluation protocol in this thesis uses 330 subjects consisting of five different kinds of cardiac disease conditions. The classifier achieved a sensitivity of 90% and a specificity of 89%. This system is ready to run on larger data sets. In EEG analysis, the search for hidden information for identification of seizures has a long history. Epilepsy is a pathological condition characterized by spontaneous and unforeseeable occurrence of seizures, during which the perception or behavior of patients is disturbed. An automatic early detection of the seizure onsets would help the patients and observers to take appropriate precautions. Various methods have been proposed to predict the onset of seizures based on EEG recordings. The use of nonlinear features motivated by the higher order spectra (HOS) has been reported to be a promising approach to differentiate between normal, background (pre-ictal) and epileptic EEG signals. In this work, these features are used to train both a Gaussian mixture model (GMM) classifier and a Support Vector Machine (SVM) classifier. Results show that the classifiers were able to achieve 93.11% and 92.67% classification accuracy, respectively, with selected HOS based features. About 2 hours of EEG recordings from 10 patients were used in this study. This thesis introduces unique bispectrum and bicoherence plots for various cardiac conditions and for normal, background and epileptic EEG signals. These plots reveal distinct patterns. The patterns are useful for visual interpretation by those without a deep understanding of spectral analysis such as medical practitioners. It includes original contributions in extracting features from HRV and EEG signals using HOS and entropy, in analyzing the statistical properties of such features on real data and in automated classification using these features with GMM and SVM classifiers.

An analytical method to solve a general class of nonlinear reactive transport models

Three recent papers published in Chemical Engineering Journal studied the solution of a model of diffusion and nonlinear reaction using three different methods. Two of these studies obtained series solutions using specialized mathematical methods, known as the Adomian decomposition method and the homotopy analysis method. Subsequently it was shown that the solution of the same particular model could be written in terms of a transcendental function called Gauss’ hypergeometric function. These three previous approaches focused on one particular reactive transport model. This particular model ignored advective transport and considered one specific reaction term only. Here we generalize these previous approaches and develop an exact analytical solution for a general class of steady state reactive transport models that incorporate (i) combined advective and diffusive transport, and (ii) any sufficiently differentiable reaction term R(C). The new solution is a convergent Maclaurin series. The Maclaurin series solution can be derived without any specialized mathematical methods nor does it necessarily involve the computation of any transcendental function. Applying the Maclaurin series solution to certain case studies shows that the previously published solutions are particular cases of the more general solution outlined here. We also demonstrate the accuracy of the Maclaurin series solution by comparing with numerical solutions for particular cases.

Valuation methods for resident funded retirement villages in Australia : a practitioner's perspective

Designed for independent living, retirement villages provide either detached or semi-detached residential dwellings with car parking and small private yards. Retirement village developments usually include a mix of independent living units (ILUs) and serviced apartments (SAs) with community facilities providing a shared congregational area for village activities and socialising. Retirement Village assets differ from traditional residential assets due to their operation in accordance with statutory legislation. In Australia, each State and Territory has its own Retirement Village Act and Regulations. In essence, the village operator provides the land and buildings to the residents who pay an amount on entry for the right of occupation. On departure from the units an agreed proportion of either the original purchase price or the sale price is paid to the outgoing resident. The market value of the operator’s interest in the Retirement Village is therefore based upon the estimated future income from Deferred Management Fees and Capital Gain upon roll-over receivable by the operator in accordance with the respective residency agreements. Given the lumpiness of these payments, there is general acceptance that the most appropriate approach to valuation is through Discounted Cash Flow (DCF) analysis. There is however inconsistency between valuers across Australia in how they undertake their DCF analysis, leading to differences in reported values and subsequent confusion among users of valuation services. To give guidance to valuers and enhance confidence from users of valuation services this paper investigates the five major elements of discounted cash flow methodology, namely cash flows, escalation factors, holding period, terminal value and discount rate. Whilst there is dissatisfaction with the financial structuring of the DMF in residency agreements, as long as there are future financial returns receivable by the Village owner/operator, then DCF will continue to be the most appropriate valuation methodology for resident funded retirement villages.

Validation Gating for Non-Linear Non-Gaussian Target Tracking

This paper develops a general theory of validation gating for non-linear non-Gaussian mod- els. Validation gates are used in target tracking to cull very unlikely measurement-to-track associa- tions, before remaining association ambiguities are handled by a more comprehensive (and expensive) data association scheme. The essential property of a gate is to accept a high percentage of correct associ- ations, thus maximising track accuracy, but provide a su±ciently tight bound to minimise the number of ambiguous associations. For linear Gaussian systems, the ellipsoidal vali- dation gate is standard, and possesses the statistical property whereby a given threshold will accept a cer- tain percentage of true associations. This property does not hold for non-linear non-Gaussian models. As a system departs from linear-Gaussian, the ellip- soid gate tends to reject a higher than expected pro- portion of correct associations and permit an excess of false ones. In this paper, the concept of the ellip- soidal gate is extended to permit correct statistics for the non-linear non-Gaussian case. The new gate is demonstrated by a bearing-only tracking example.

Body-site distribution of skin cancer, pre-malignant and common benign pigmented lesions excised in general practice

Background Concern about skin cancer is a common reason for people from predominantly fair-skinned populations to present to primary care doctors. Objectives To examine the frequency and body-site distribution of malignant, pre-malignant and benign pigmented skin lesions excised in primary care. Methods This prospective study conducted in Queensland, Australia, included 154 primary care doctors. For all excised or biopsied lesions, doctors recorded the patient's age and sex, body site, level of patient pressure to excise, and the clinical diagnosis. Histological confirmation was obtained through pathology laboratories. Results Of 9650 skin lesions, 57·7% were excised in males and 75·0% excised in patients ≥50years. The most common diagnoses were basal cell carcinoma (BCC) (35·1%) and squamous cell carcinoma (SCC) (19·7%). Compared with the whole body, the highest densities for SCC, BCC and actinic keratoses were observed on chronically sun-exposed areas of the body including the face in males and females, the scalp and ears in males, and the hands in females. The density of BCC was also high on intermittently or rarely exposed body sites. Females, younger patients and patients with melanocytic naevi were significantly more likely to exert moderate/high levels of pressure on the doctor to excise. Conclusions More than half the excised lesions were skin cancer, which mostly occurred on the more chronically sun-exposed areas of the body. Information on the type and body-site distribution of skin lesions can aid in the diagnosis and planned management of skin cancer and other skin lesions commonly presented in primary care.

The impact of temperature on mortality in Tianjin, China : a case-crossover design with a distributed lag non-linear model

Background There has been increasing interest in assessing the impacts of temperature on mortality. However, few studies have used a case–crossover design to examine non-linear and distributed lag effects of temperature on mortality. Additionally, little evidence is available on the temperature-mortality relationship in China, or what temperature measure is the best predictor of mortality. Objectives To use a distributed lag non-linear model (DLNM) as a part of case–crossover design. To examine the non-linear and distributed lag effects of temperature on mortality in Tianjin, China. To explore which temperature measure is the best predictor of mortality; Methods: The DLNM was applied to a case¬−crossover design to assess the non-linear and delayed effects of temperatures (maximum, mean and minimum) on deaths (non-accidental, cardiopulmonary, cardiovascular and respiratory). Results A U-shaped relationship was consistently found between temperature and mortality. Cold effects (significantly increased mortality associated with low temperatures) were delayed by 3 days, and persisted for 10 days. Hot effects (significantly increased mortality associated with high temperatures) were acute and lasted for three days, and were followed by mortality displacement for non-accidental, cardiopulmonary, and cardiovascular deaths. Mean temperature was a better predictor of mortality (based on model fit) than maximum or minimum temperature. Conclusions In Tianjin, extreme cold and hot temperatures increased the risk of mortality. Results suggest that the effects of cold last longer than the effects of heat. It is possible to combine the case−crossover design with DLNMs. This allows the case−crossover design to flexibly estimate the non-linear and delayed effects of temperature (or air pollution) whilst controlling for season.

Numerical methods for second-order stochastic differential equations

We seek numerical methods for second‐order stochastic differential equations that reproduce the stationary density accurately for all values of damping. A complete analysis is possible for scalar linear second‐order equations (damped harmonic oscillators with additive noise), where the statistics are Gaussian and can be calculated exactly in the continuous‐time and discrete‐time cases. A matrix equation is given for the stationary variances and correlation for methods using one Gaussian random variable per timestep. The only Runge–Kutta method with a nonsingular tableau matrix that gives the exact steady state density for all values of damping is the implicit midpoint rule. Numerical experiments, comparing the implicit midpoint rule with Heun and leapfrog methods on nonlinear equations with additive or multiplicative noise, produce behavior similar to the linear case.

Physical activity, sitting and depression during pregnancy

Aims The aim of this cross sectional study is to explore levels of physical activity and sitting behaviour amongst a sample of pregnant Australian women (n = 81), and investigate whether reported levels of physical activity and/or time spent sitting were associated with depressive symptom scores after controlling for potential covariates. Methods Study participants were women who attended the antenatal clinic of a large Brisbane maternity hospital between October and November 2006. Data relating to participants. current levels of physical activity, sitting behaviour, depressive symptoms, demographic characteristics and exposure to known risk factors for depression during pregnancy were collected; via on-site survey, follow-up telephone interview (approximately one week later) and post delivery access to participant hospital records. Results Participants were aged 29.5 (¡¾ 5.6) years and mostly partnered (86.4%) with a gross household income above $26,000 per annum (88.9%). Levels of physical activity were generally low, with only 28.4 % of participants reporting sufficient total activity and 16% of participants reporting sufficient planned (leisure-time) activity. The sample mean for depressive symptom scores measured by the Hospital Anxiety and Depression Scale (HADS-D) was 6.38 (¡¾ 2.55). The mean depressive symptom scores for participants who reported total moderate-to-vigorous activity levels of sufficient, insufficient, and none, were 5.43 (¡¾ 1.56), 5.82 (¡¾ 1.77) and 7.63 (¡¾ 3.25), respectively. Hierarchical multivariable linear regression modelling indicated that after controlling for covariates, a statistically significant difference of 1.09 points was observed between mean depressive symptom scores of participants who reported sufficient total physical activity, compared with participants who reported they were engaging in no moderate-to-vigorous activity in a typical week (p = 0.05) but this did not reach the criteria for a clinically meaningful difference. Total physical activity was contributed 2.2% to the total 30.3% of explained variance within this model. The other main contributors to explained variance in multivariable regression models were anxiety symptom scores and the number of existing children. Further, a trend was observed between higher levels of planned sitting behaviour and higher depressive symptom scores (p = 0.06); this correlation was not clinically meaningful. Planned sitting contributed 3.2% to the total 31.3 % of explained variance. The number of regression covariates and limited sample size led to a less than ideal ratio of covariates to participants, probably attenuating this relationship. Specific information about the sitting-based activities in which participants engaged may have provided greater insight about the relationship between planned sitting and depressive symptoms, but these data were not captured by the present study. Conclusions The finding that higher levels of physical activity were associated with lower levels of depressive symptoms is consistent with the current body of existing literature in pregnant women, and with a larger body of evidence based in general population samples. Although this result was not considered clinically meaningful, the criterion for a clinically meaningful result was an a priori decision based on quality of life literature in non-pregnant populations and may not truly reflect a difference in symptoms that is meaningful to pregnant women. Further investigation to establish clinically meaningful criteria for continuous depressive symptom data in pregnant women is required. This result may have implications relating to prevention and management options for depression during pregnancy. The observed trend between planned sitting and depressive symptom scores is consistent with literature based on leisure-time sitting behaviour in general population samples, and suggests that further research in this area, with larger samples of pregnant women and more specific sitting data is required to explore potential associations between activities such as television viewing and depressive symptoms, as this may be an area of behaviour that is amenable to modification.

Linear models for endocytic transformations from live cell imaging

Endocytosis is the process by which cells internalise molecules including nutrient proteins from the extracellular media. In one form, macropinocytosis, the membrane at the cell surface ruffles and folds over to give rise to an internalised vesicle. Negatively charged phospholipids within the membrane called phosphoinositides then undergo a series of transformations that are critical for the correct trafficking of the vesicle within the cell, and which are often pirated by pathogens such as Salmonella. Advanced fluorescent video microscopy imaging now allows the detailed observation and quantification of these events in live cells over time. Here we use these observations as a basis for building differential equation models of the transformations. An initial investigation of these interactions was modelled with reaction rates proportional to the sum of the concentrations of the individual constituents. A first order linear system for the concentrations results. The structure of the system enables analytical expressions to be obtained and the problem becomes one of determining the reaction rates which generate the observed data plots. We present results with reaction rates which capture the general behaviour of the reactions so that we now have a complete mathematical model of phosphoinositide transformations that fits the experimental observations. Some excellent fits are obtained with modulated exponential functions; however, these are not solutions of the linear system. The question arises as to how the model may be modified to obtain a system whose solution provides a more accurate fit.