Statistical Monitoring of Dynamic Multivariate Processes: Part I: Modeling Auto- and Cross-Correlation

The work in this paper is of particular significance since it considers the problem of modelling cross- and auto-correlation in statistical process monitoring. The presence of both types of correlation can lead to fault insensitivity or false alarms, although in published literature to date, only autocorrelation has been broadly considered. The proposed method, which uses a Kalman innovation model, effectively removes both correlations. The paper (and Part 2 [2]) has emerged from work supported by EPSRC grant GR/S84354/01 and is of direct relevance to problems in several application areas including chemical, electrical, and mechanical process monitoring.

Fully differential cross sections for transfer ionization - a sensitive probe of high level correlation effects in atoms

The transfer ionization process offers a unique opportunity to study radial and angular electron correlations in the helium atom. We report calculations for the multiple differential cross sections of the transfer ionization process p + He --> H + He++ + e(-). The results of these calculations demonstrate the strong sensitivity of the fully differential cross sections to fine details of electron correlation in the target atom. Specifically, angular electron correlation in the ground state of helium results in a broad peak in the electron emission spectra in the backward direction, relative to the incoming beam. Our model explains some of the key effects observed in measurements of multiple differential cross sections using the COLTRIMS technique.

Revealing the effect of angular correlation in the ground-state He wavefunction: a coincidence study of the transfer ionization process

A joint theoretical-experimental study of the transfer ionization process p + He -> H-0 + He2+ + e(-) is presented. For the first time all particles in the final state have been detected in triple coincidence. This fully differential measurement is in good agreement with a theoretical model where the target is described by a wavefunction containing both radial and angular correlation terms.

Escape times for rigid Brownian rotators in a bistable potential from the time evolution of the Green function and the characteristic time of the probability evolution

The greatest relaxation time for an assembly of three- dimensional rigid rotators in an axially symmetric bistable potential is obtained exactly in terms of continued fractions as a sum of the zero frequency decay functions (averages of the Legendre polynomials) of the system. This is accomplished by studying the entire time evolution of the Green function (transition probability) by expanding the time dependent distribution as a Fourier series and proceeding to the zero frequency limit of the Laplace transform of that distribution. The procedure is entirely analogous to the calculation of the characteristic time of the probability evolution (the integral of the configuration space probability density function with respect to the position co-ordinate) for a particle undergoing translational diffusion in a potential; a concept originally used by Malakhov and Pankratov (Physica A 229 (1996) 109). This procedure allowed them to obtain exact solutions of the Kramers one-dimensional translational escape rate problem for piecewise parabolic potentials. The solution was accomplished by posing the problem in terms of the appropriate Sturm-Liouville equation which could be solved in terms of the parabolic cylinder functions. The method (as applied to rotational problems and posed in terms of recurrence relations for the decay functions, i.e., the Brinkman approach c.f. Blomberg, Physica A 86 (1977) 49, as opposed to the Sturm-Liouville one) demonstrates clearly that the greatest relaxation time unlike the integral relaxation time which is governed by a single decay function (albeit coupled to all the others in non-linear fashion via the underlying recurrence relation) is governed by a sum of decay functions. The method is easily generalized to multidimensional state spaces by matrix continued fraction methods allowing one to treat non-axially symmetric potentials, where the distribution function is governed by two state variables. (C) 2001 Elsevier Science B.V. All rights reserved.

Factors affecting adherence to use of hip protectors amongst residents of nursing homes - A correlation study

Background: Hip protectors are protective pads designed to cover the greater trochanter and attenuate or disperse the force of a fall sufficiently to prevent a hip fracture. Promising results from randomised controlled trials in nursing homes have resulted in hip protectors being widely recommended in the health care literature and in national guidelines. Objectives: The objectives of the study were to identify characteristics of individual residents, and the organisational features of the homes in which they live, which may affect adherence to wearing hip protectors. Design: An observational, correlation study designed to identify factors related to adherence. Setting: Forty nursing and residential homes in the UK. Participants: 1346 residents of the homes who were not confined to bed and with no pressure sore on the hip. Methods: The introduction of an evidence-based policy to offer Safehips hip protectors to residents free of charge and with support from a nurse facilitator. Adherence to wearing the hip protectors was observed over 72 weeks. Results: Initial acceptance of the hip protectors was 37.2%. Continued adherence was 23.9% at 24 weeks; 23.2% at 48 weeks; and 19.9% at 72 weeks. Greater adherence was associated with the following individual resident characteristics: a greater degree of dependency (95% CI 1.39 - m3.78) and cognitive impairment (95% CI 1.01 - 2.98); being male rather than female (95% CI 1.06 - 2.48). Greater adherence was also associated with the following organisational characteristics of homes: fewer changes of senior manager during the study period (95% CI 1.01 - 8.51), and being resident in a home with a resident profile showing a greater proportion of residents with a higher degree of dependency (95% CI 1.04 - 1.27). There was wide a variation in the degree of success in implementation between homes (adherence of 0 - 100% at 24 weeks). Conclusions: Those implementing a policy of introducing hip protectors into nursing and residential homes should consider targeting residents with cognitive impairment. Such residents are at greater risk of hip fracture and appear to be more likely to continue wearing hip protectors. Those charged with implementing changes inpractice or policy should consider how the context for implementation can be optimised to increase the likelihood of success.

Correlation Effects in the Compton Profile of Silicon

Ab initio nonlocal pseudopotential variational quantum Monte Carlo techniques are used to compute the correlation effects on the valence momentum density and Compton profile of silicon. Our results for this case are in excellent agreement with the Lam-Platzman correction computed within the local density approximation. Within the approximations used, we rule out valence electron correlations as the dominant source of discrepancies between calculated and measured Compton profiles of silicon.

Resting and daily energy expenditures of free-living field voles are positively correlated but reflect extrinsic rather than intrinsic effects

Resting metabolic rates at thermoneutral (RMRts) are unexpectedly variable. One explanation is that high RMRts intrinsically potentiate a greater total daily energy expenditure (DEE), but recent work has suggested that DEE is extrinsically defined by the environment, which independently affects RMRt. This extrinsic effect could occur because expenditure is forced upwards in poor habitats or enabled to rise in good habitats. We provide here an intraspecific test for an association between RMRt and DEE that separates intrinsic from extrinsic effects and forcing from enabling effects. We measured the DEE and RMRt of 75 free-living short-tailed field voles at two time points in late winter. Across all sites, there was a positive link between individual variation in RMRt and DEE. This correlation, however, emerged only because of an effect across sites, rather than because of an intrinsic association within sites. We defined site quality from the survivorship of voles at the sites and the time at which they commenced breeding in spring. The associations between DEE/RMRt and site quality suggested that in February voles in poorer sites had higher energy demands, indicating that DEE was forced upwards, but in March the opposite was true, with higher demands in good sites, indicating that high expenditure was enabled. These data show that daily energy demands are extrinsically defined, with a link to RMRt that is secondary or independent. Both forcing and enabling effects of the environment may pertain at different times of year.