Kinematics and uncertainty relations of a quantum test particle in a curved space-time

A possible model for quantum kinematics of a test particle in a curved space-time is proposed. Every reasonable neighbourhood V_e of a curved space-time can be equipped with a nonassociative binary operation called the geodesic multiplication of space-time points. In the case of the Minkowski space-time, left and right translations of the geodesic multiplication coincide and amount to a rigid shift of the space-time x->x+a. In a curved space-time infinitesimal geodesic right translations can be used to define the (geodesic) momentum operators. The commutation relations of position and momentum operators are taken as the quantum kinematic algebra. As an example, detailed calculations are performed for the space-time of a weak plane gravitational wave. The uncertainty relations following from the commutation rules are derived and their physical meaning is discussed.Comment: 6 pages, LaTeX, talk given in the session ``Quantum Fields in Curved Space'' at the VIII Marcel Grossmann Conference in Jerusalem, Israel, June 199

Monitoring Processes with Changing Variances

Statistical process control (SPC) has evolved beyond its classical applications in manufacturing to monitoring economic and social phenomena. This extension requires consideration of autocorrelated and possibly non-stationary time series. Less attention has been paid to the possibility that the variance of the process may also change over time. In this paper we use the innovations state space modeling framework to develop conditionally heteroscedastic models. We provide examples to show that the incorrect use of homoscedastic models may lead to erroneous decisions about the nature of the process. The framework is extended to include counts data, when we also introduce a new type of chart, the P-value chart, to accommodate the changes in distributional form from one period to the next.control charts, count data, GARCH, heteroscedasticity, innovations, state space, statistical process control

Is level of neighbourhood green space associated with physical activity in green space?

Background There is accumulating evidence that greater availability of green space in a neighbourhood is associated with health benefits for the local population. One mechanism proposed for this association is that green space provides a venue for, and therefore encourages, physical activity. It has also been suggested that socio-economic health inequalities may be narrower in greener areas because of the equalised opportunity for physical activity green spaces provide. However, research exploring associations between the availability of green space and physical activity has produced mixed results. Limits to the assessment of the type and amount of physical activity which occurs specifically in green space may account for these mixed findings. This observational study was therefore concerned with the extent to which green space is a venue for physical activity and whether this could account for narrower socio-economic health inequalities in greener neighbourhoods.<p></p> Method Secondary analysis of cross sectional data on 3679 adults (16+) living in urban areas across Scotland matched with a neighbourhood level measure of green space availability. Associations between green space availability and both total physical activity, and activity specifically within green space, were explored using logistic regression models. Interactions between socio-economic position and physical activity were assessed. All models adjusted for age, sex and household income.<p></p> Results The availability of green space in a neighbourhood was not associated with total physical activity or that specifically in green space. There was no evidence that income-related inequalities in physical activity within green space were narrower in greener areas of Scotland.<p></p> Conclusion Physical activity may not be the main mechanism explaining the association between green space and health in Scotland. The direct effect of perceiving a natural environment on physiological and psychological health may offer an alternative explanation.<p></p&gt

Exponential smoothing and non-negative data

The most common forecasting methods in business are based on exponential smoothing and the most common time series in business are inherently non-negative. Therefore it is of interest to consider the properties of the potential stochastic models underlying exponential smoothing when applied to non-negative data. We explore exponential smoothing state space models for non-negative data under various assumptions about the innovations, or error, process. We first demonstrate that prediction distributions from some commonly used state space models may have an infinite variance beyond a certain forecasting horizon. For multiplicative error models which do not have this flaw, we show that sample paths will converge almost surely to zero even when the error distribution is non-Gaussian. We propose a new model with similar properties to exponential smoothing, but which does not have these problems, and we develop some distributional properties for our new model. We then explore the implications of our results for inference, and compare the short-term forecasting performance of the various models using data on the weekly sales of over three hundred items of costume jewelry. The main findings of the research are that the Gaussian approximation is adequate for estimation and one-step-ahead forecasting. However, as the forecasting horizon increases, the approximate prediction intervals become increasingly problematic. When the model is to be used for simulation purposes, a suitably specified scheme must be employed.forecasting; time series; exponential smoothing; positive-valued processes; seasonality; state space models.

Microarray analysis of pathways involved in bladder cancer invasion and metastasis.

MDHypoxia-inducible genes have been linked to the aggressive phenotype of cancer. However, nearly all work on hypoxia-regulated genes has been conducted in vitro on cell lines. Here the hypoxia transcriptome in primary human bladder cancer was investigated using cIDNA microarrays to compare genes induced by hypoxia in vitro in bladder cancer cell line EJ28 with genes upregulated on an in vivo array of 39 bladder tumours (27 Ta/T1 12 T2-T4). mRNA array fold-changes were correlated with carbonic anhydrase IX (CA IX) staining and necrosis of tumours as surrogate markers of hypoxia. Of 6000 genes 32 were repeatedly hypoxia-inducible in vitro more than 2-fold, five of which were novel, including lactate transporter SLC16A3 and RNAse 4. Eight of 32 hypoxia-inducible genes in vitro were also upregulated on the vivo array. Vascular endothelial growth factor (VEGF) mRNA was upregulated 2-fold by hypoxia and 2 to 18-fold in 31/39 tumours. Also up regulated on both arrays was GLUT 1 mRNA, and fold changes on the in vivo genearray significantly correlated with CA IX staining of tumours (p=0.008). However Insulin-like growth factor binding protein 3 (IGFBP-3) mRNA was the most strongly differentially expressed gene in both arrays and its upregulation was confirmed in the urine of bladder cancer patients (n=157, p<0.01) and in cell line supernatants. Angiogenin was also upregulated in urine of bladder cancer patients. Selected genes upregulated by hypoxia (HIF la, HIF 2a, CA IX and NIP3) were studied by immunohistochemistry for their prognostic significance and association with necrosis in 98 cystectomy specimens. Normal human urothelial cells were also grown in culture and a hypoxia genearray profile compared with EJ28, peripheral blood monocytes and T-cells. This thesis studies the prevalence of hypoxia and necrosis in bladder cancer, its relationship with prognosis, genes associated with the hypoxic phenotype and hypoxia related molecular pathways

Evidence for alignment of the rotation and velocity vectors in pulsars. II. Further data and emission heights

We have conducted observations of 22 pulsars at frequencies of 0.7, 1.4 and 3.1 GHz and present their polarization profiles. The observations were carried out for two main purposes. First we compare the orientation of the spin and velocity vectors to verify the proposed alignment of these vectors by Johnston et al. (2005). We find, for the 14 pulsars for which we were able to determine both vectors, that 7 are plausibly aligned, a fraction which is lower than, but consistent with, earlier measurements. Secondly, we use profiles obtained simultaneously at widely spaced frequencies to compute the radio emission heights. We find, similar to other workers in the field, that radiation from the centre of the profile originates from lower in the magnetosphere than the radiation from the outer parts of the profile.Comment: Accepted by MNRAS. 14 page

Exponential Smoothing for Inventory Control: Means and Variances of Lead-Time Demand

Exponential smoothing is often used to forecast lead-time demand for inventory control. In this paper, formulae are provided for calculating means and variances of lead-time demand for a wide variety of exponential smoothing methods. A feature of many of the formulae is that variances, as well as the means, depend on trends and seasonal effects. Thus, these formulae provide the opportunity to implement methods that ensure that safety stocks adjust to changes in trend or changes in season.Forecasting; inventory control; lead-time demand; exponential smoothing; forecast variance.

Monitoring Processes with Changing Variances

Statistical process control (SPC) has evolved beyond its classical applications in manufacturing to monitoring economic and social phenomena. This extension requires consideration of autocorrelated and possibly non-stationary time series. Less attention has been paid to the possibility that the variance of the process may also change over time. In this paper we use the innovations state space modeling framework to develop conditionally heteroscedastic models. We provide examples to show that the incorrect use of homoscedastic models may lead to erroneous decisions about the nature of the process. The framework is extended to include counts data, when we also introduce a new type of chart, the P-value chart, to accommodate the changes in distributional form from one period to the next.Control charts, count data, GARCH, heteroscedasticity, innovations, state space, statistical process control