Large and Moderate Deviations Principles for Recursive Kernel Estimator of a Multivariate Density and its Partial Derivatives

2000 Mathematics Subject Classification: 62G07, 60F10.

On slowdown and speedup of transient random walks in random environment

We consider one-dimensional random walks in random environment which are transient to the right. Our main interest is in the study of the sub-ballistic regime, where at time n the particle is typically at a distance of order O(n (kappa) ) from the origin, kappa is an element of (0, 1). We investigate the probabilities of moderate deviations from this behaviour. Specifically, we are interested in quenched and annealed probabilities of slowdown (at time n, the particle is at a distance of order O (n (nu 0)) from the origin, nu(0) is an element of (0, kappa)), and speedup (at time n, the particle is at a distance of order n (nu 1) from the origin , nu(1) is an element of (kappa, 1)), for the current location of the particle and for the hitting times. Also, we study probabilities of backtracking: at time n, the particle is located around (-n (nu) ), thus making an unusual excursion to the left. For the slowdown, our results are valid in the ballistic case as well.

Moderate sleep restriction in treated older male OSA participants: Greater impairment during monotonous driving compared with controls

Objectives To examine the effects on monotonous driving of normal sleep versus one night of sleep restriction in continuous positive airway pressure (CPAP) treated obstructive sleep apnoea (OSA) patients compared with age matched healthy controls. Methods Nineteen CPAP treated compliant male OSA patients (OSA-treated patients (OPs)), aged 50–75 years, and 20 healthy age-matched controls underwent both a normal night’s sleep and sleep restriction to 5 h (OPs remained on CPAP) in a counterbalanced design. All participants completed a 2 h afternoon monotonous drive in a realistic car simulator. Driving was monitored for sleepiness-related minor and major lane deviations, with ‘safe’ driving time being total time driven prior to first major lane deviation. EEGs were recorded continuously, and subjective sleepiness ratings were taken at regular intervals throughout the drive. Results After a normal night’s sleep, OPs and controls did not differ in terms of driving performance or in their ability to assess the levels of their own sleepiness, with both groups driving ‘safely’ for approximately 90 min. However, after sleep restriction, OPs had a significantly shorter (65 min) safe driving time and had to apply more compensatory effort to maintain their alertness compared with controls. They also underestimated the enhanced sleepiness. Nevertheless, apart from this caveat, there were generally close associations between subjective sleepiness, likelihood of a major lane deviation and EEG changes indicative of sleepiness. Conclusions With a normal night’s sleep, effectively treated older men with OSA drive as safely as healthy men of the same age. However, after restricted sleep, driving impairment is worse than that of controls. This suggests that, although successful CPAP treatment can alleviate potential detrimental effects of OSA on monotonous driving following normal sleep, these patients remain more vulnerable to sleep restriction.

Systematic variations in polymer gel dosimeter calibration due to container influence and deviations from water equivalence

There are a number of gel dosimeter calibration methods in contemporary usage. The present study is a detailed Monte Carlo investigation into the accuracy of several calibration techniques. Results show that for most arrangements the dose to gel accurately reflects the dose to water, with the most accurate method involving the use of a large diameter flask of gel into which multiple small fields of varying dose are directed. The least accurate method was found to be that of a long test tube in a water phantom, coaxial with the beam. The large flask method is also the most straightforward and least likely to introduce errors during setup, though, to its detriment, the volume of gel required is much more than other methods.

Peripheral ocular aberrations in mild and moderate keratoconus

Purpose: To investigate the influence of keratoconus on peripheral ocular aberrations. Methods: Aberrations of 7 mild and 5 moderate keratoconics were determined over a 42°horizontal x 32° vertical visual field with a modified COAS-HD aberrometer. Control data were obtained from an emmetropic group. Results: Most aberrations in keratoconics showed field dependence predominately along the vertical meridian. Mean spherical equivalent M, oblique astigmatism J45 and regular astigmatism J180 refraction components and total root mean square aberrations (excluding defocus) had high magnitudes in the inferior visual field. The rates of change of aberrations were higher in moderate than in mild keratoconics. Coma was the dominant peripheral higher-order aberration in both emmetropes and keratoconics; for the latter it had high magnitudes in the centre and periphery of the visual field. Conclusion: Greater rates of change of aberrations across the visual field occurred for the keratoconic groups than for the emmetropic control group. Moderate keratoconics had more rapid changes in, and higher magnitudes of aberrations across the visual field than mild keratoconics. The dominant higher-order aberration for the keratoconics across the visual field was vertical coma.

Testing and simulation of extruded polystyrene foam at low to moderate strain rates

This paper presents a study into the behaviour of extruded polystyrene foam at low strain rates. The foam is being studied in order assess its potential for use as part of a new innovative design of portable road safety barrier the aim to consume less water and reduce rates of serious injury. The foam was tested at a range of low strain rates, with the stress and strain behaviour of the foam specimens being recorded. The energy absorption capabilities of the foam were assessed as well as the response of the foam to multiple loadings. The experimental data was then used to create a material model of the foam for use in the explicit finite element solver LS-DYNA. Simulations were carried out using the material model which showed excellent correlation between the numerical material model and the experimental data.

Turbulence characteristics of a small subtropical estuary during and after some moderate rainfall

In natural estuaries, scalar diffusion and dispersion are driven by turbulence. In the present study, detailed turbulence measurements were conducted in a small subtropical estuary with semi-diurnal tides under neap tide conditions. Three acoustic Doppler velocimeters were installed mid-estuary at fixed locations close together. The units were sampled simultaneously and continuously at relatively high frequency for 50 h. The results illustrated the influence of tidal forcing in the small estuary, although low frequency longitudinal velocity oscillations were observed and believed to be induced by external resonance. The boundary shear stress data implied that the turbulent shear in the lower flow region was one order of magnitude larger than the boundary shear itself. The observation differed from turbulence data in a laboratory channel, but a key feature of natural estuary flow was the significant three dimensional effects associated with strong secondary currents including transverse shear events. The velocity covariances and triple correlations, as well as the backscatter intensity and covariances, were calculated for the entire field study. The covariances of the longitudinal velocity component showed some tidal trend, while the covariances of the transverse horizontal velocity component exhibited trends that reflected changes in secondary current patterns between ebb and flood tides. The triple correlation data tended to show some differences between ebb and flood tides. The acoustic backscatter intensity data were characterised by large fluctuations during the entire study, with dimensionless fluctuation intensity I0b =Ib between 0.46 and 0.54. An unusual feature of the field study was some moderate rainfall prior to and during the first part of the sampling period. Visual observations showed some surface scars and marked channels, while some mini transient fronts were observed.

Even moderate visual impairments degrade drivers’ ability to see pedestrians at night

Purpose: To determine the effect of moderate levels of refractive blur and simulated cataracts on nighttime pedestrian conspicuity in the presence and absence of headlamp glare. Methods: The ability to recognize pedestrians at night was measured in 28 young adults (M=27.6 years) under three visual conditions: normal vision, refractive blur and simulated cataracts; mean acuity was 20/40 or better in all conditions. Pedestrian recognition distances were recorded while participants drove an instrumented vehicle along a closed road course at night. Pedestrians wore one of three clothing conditions and oncoming headlamps were present for 16 participants and absent for 12 participants. Results: Simulated visual impairment and glare significantly reduced the frequency with which drivers recognized pedestrians and the distance at which the drivers first recognized them. Simulated cataracts were significantly more disruptive than blur even though photopic visual acuity levels were matched. With normal vision, drivers responded to pedestrians at 3.6x and 5.5x longer distances on average than for the blur or cataract conditions, respectively. Even in the presence of visual impairment and glare, pedestrians were recognized more often and at longer distances when they wore a “biological motion” reflective clothing configuration than when they wore a reflective vest or black clothing. Conclusions: Drivers’ ability to recognize pedestrians at night is degraded by common visual impairments even when the drivers’ mean visual acuity meets licensing requirements. To maximize drivers’ ability to see pedestrians, drivers should wear their optimum optical correction, and cataract surgery should be performed early enough to avoid potentially dangerous reductions in visual performance.