Numerical simulation of the Riesz fractional diffusion equation with a nonlinear source term

In this paper, A Riesz fractional diffusion equation with a nonlinear source term (RFDE-NST) is considered. This equation is commonly used to model the growth and spreading of biological species. According to the equivalent of the Riemann-Liouville(R-L) and Gr¨unwald-Letnikov(GL) fractional derivative definitions, an implicit difference approximation (IFDA) for the RFDE-NST is derived. We prove the IFDA is unconditionally stable and convergent. In order to evaluate the efficiency of the IFDA, a comparison with a fractional method of lines (FMOL) is used. Finally, two numerical examples are presented to show that the numerical results are in good agreement with our theoretical analysis.

Comparison of three expert elicitation methods for logistic regression on predicting the presence of the threatened brush-tailed rock-wallaby petrogale penicillata

Numerous expert elicitation methods have been suggested for generalised linear models (GLMs). This paper compares three relatively new approaches to eliciting expert knowledge in a form suitable for Bayesian logistic regression. These methods were trialled on two experts in order to model the habitat suitability of the threatened Australian brush-tailed rock-wallaby (Petrogale penicillata). The first elicitation approach is a geographically assisted indirect predictive method with a geographic information system (GIS) interface. The second approach is a predictive indirect method which uses an interactive graphical tool. The third method uses a questionnaire to elicit expert knowledge directly about the impact of a habitat variable on the response. Two variables (slope and aspect) are used to examine prior and posterior distributions of the three methods. The results indicate that there are some similarities and dissimilarities between the expert informed priors of the two experts formulated from the different approaches. The choice of elicitation method depends on the statistical knowledge of the expert, their mapping skills, time constraints, accessibility to experts and funding available. This trial reveals that expert knowledge can be important when modelling rare event data, such as threatened species, because experts can provide additional information that may not be represented in the dataset. However care must be taken with the way in which this information is elicited and formulated.

The efficacy of the Sortino ratio and other benchmarked performance measures under skewed return distributions

This paper will investigate the suitability of existing performance measures under the assumption of a clearly defined benchmark. A range of measures are examined including the Sortino Ratio, the Sharpe Selection ratio (SSR), the Student’s t-test and a decay rate measure. A simulation study is used to assess the power and bias of these measures based on variations in sample size and mean performance of two simulated funds. The Sortino Ratio is found to be the superior performance measure exhibiting more power and less bias than the SSR when the distribution of excess returns are skewed.

POOR ICARUS CHARMIAN : Review of The Life and Myth of Charmian Clift by Nadia Wheatley (2001) online

Online Review

Raman spectroscopic study of the antimonate mineral bahianite Al5Sb35+O14(OH)2

Raman spectroscopy has been used to characterise the antimonate mineral bahianite Al5Sb35+O14(OH)2 , a semi-precious gem stone. The mineral is characterised by an intense Raman band at 818 cm-1 assigned to Sb3O1413- stretching vibrations. Other lower intensity bands at 843 and 856 cm-1 are also assigned to this vibration and this concept suggests the non-equivalence of SbO units in the structure. Low intensity Raman bands at 669 and 682 cm-1 are probably assignable to the OSbO antisymmetric stretching vibrations. Raman bands at 1756, 1808 and 1929 cm-1 may be assigned to δ SbOH deformation modes, whilst Raman bands at 3462 and 3495 cm-1 are assigned to AlOH stretching vibrations. Complexity in the low wave number region is attributed to the composition of the mineral.

Raman spectroscopic study of the phosphate mineral Churchite-(Y) YPO4.2H2O

Raman spectroscopy has been used to study the rare earth mineral churchite-(Y) of formula (Y,REE)(PO4) •2H2O. The mineral contains yttrium and depending on the locality, a range of rare earth metals. The Raman spectra of two churchite-(Y) mineral samples from Jáchymov and Medvědín in the Czech Republic were compared with the Raman spectra of churchite-(Y) downloaded from the RRUFF data base. The Raman spectra of churchite-(Y) are characterized by an intense sharp band at 975 cm-1 assigned to the ν1 (PO4)3- symmetric stretching mode. A lower intensity band observed at around 1065 cm-1 is attributed to the ν3 (PO43-) antisymmetric stretching mode. The (PO43-) bending modes are observed at 497 cm-1 (ν2) and 563 cm-1(ν4). Some small differences in the band positions between the four churchite-(Y) samples from four different localities were found. These differences are possible to explain as different compositions of the churchite-(Y) minerals.

An empirical investigation of the level effect in Australian interest rates

An extensive literature examines the dynamics of interest rates, with particular attention given to the positive relationship between interest-rate volatility and the level of interest rates—the so-called level effect. This paper examines the interaction between the estimated level effect and competing parameterisations of interest-rate volatility for the Australian yield curve. We adopt a new methodology that estimates elasticity in a multivariate setting that explicitly accommodates the correlations that exist between various yield factors. Results show that significant correlations exist between the residuals of yield factors and that such correlations do indeed impact on model estimates. Within the multivariate setting, the level of the short rate is shown to be a crucial determinant of the conditional volatility of all three yield factors. Measures of model fit suggest that, in addition to the usual level effect, the incorporation of GARCH effects and possible regime shifts is important

The distribution of the sample minimum-variance frontier

In this paper, we present a finite sample analysis of the sample minimum-variance frontier under the assumption that the returns are independent and multivariate normally distributed. We show that the sample minimum-variance frontier is a highly biased estimator of the population frontier, and we propose an improved estimator of the population frontier. In addition, we provide the exact distribution of the out-of-sample mean and variance of sample minimum-variance portfolios. This allows us to understand the impact of estimation error on the performance of in-sample optimal portfolios. Key Words: minimum-variance frontier; efficiency set constants; finite sample distribution

The call of the road : factors predicting students' car travelling intentions and behaviour

The most common daily trip for employed persons and students is the commute to and from work and/or place of study. Though there are clear environmental, health and safety benefits from using public transport instead of private vehicles for these trips, a high proportion of commuters still choose private vehicles to get to work or study. This study reports an investigation of psychological factors influencing students’ travel choices from the perspective of the Theory of Planned Behaviour (TPB). Students from 3 different university campuses (n= 186) completed a cross-sectional survey on their car commuting behaviour. Particular focus was given to whether car commuting habits could add to understanding of commuting behaviour over and above behavioural intentions. Results indicated that, as expected, behavioural intention to travel by car was the strongest TPB predictor of car commuting behaviour. Further, general car commuting habits explained additional variance over and above TPB constructs, though the contribution was modest. No relationship between habit and intentions was found. Overall results suggest that, although student car commuting behaviour is habitual in nature, it is predominantly guided by reasoned action. Implications of these findings are that in order to alter the use of private vehicles, the factors influencing commuters’ intentions to travel by car must be addressed. Specifically, interventions should target the perceived high levels of both the acceptability of commuting by car and the perceived control over the choice to commute by car.