Convergence of the kk-Means Minimization Problem using Γ\Gamma-Convergence

The $k$-means method is an iterative clustering algorithm which associates each observation with one of $k$ clusters. It traditionally employs cluster centers in the same space as the observed data. By relaxing this requirement, it is possible to apply the $k$-means method to infinite dimensional problems, for example multiple target tracking and smoothing problems in the presence of unknown data association. Via a $\Gamma$-convergence argument, the associated optimization problem is shown to converge in the sense that both the $k$-means minimum and minimizers converge in the large data limit to quantities which depend upon the observed data only through its distribution. The theory is supplemented with two examples to demonstrate the range of problems now accessible by the $k$-means method. The first example combines a non-parametric smoothing problem with unknown data association. The second addresses tracking using sparse data from a network of passive sensors

Using extreme value theory to evaluate the leading pedestrian interval road safety intervention

Improving road safety is hugely important with the number of deaths on the world's roads remaining unacceptably high; an estimated 1.35 million people die each year as a result of road traffic collisions (WHO, 2020). Current practice for treating collision hotspots is almost always reactive: once a threshold level of collisions has been overtopped during some pre-determined observation period, treatment is applied (e.g. road safety cameras). Traffic collisions are rare, so prolonged observation periods are necessary. However, traffic conflicts are more frequent and are a margin of the social cost; hence, traffic conflict before/after studies can be conducted over shorter time periods. We investigate the effect of implementing the leading pedestrian interval (LPI) treatment (Van Houten et al. 2000) at signalised intersections as a safety intervention in a city in north America. Pedestrian-vehicle traffic conflict data were collected from treatment and control sites during the before and after periods. We implement a before/after study on post-encroachment times (PETs) where small PET values denote a near-miss. Hence, extreme value theory is employed to model extremes of our PET processes, with adjustments to the usual modelling framework to account for temporal dependence and treatment effects.Comment: 16 page

Public attitudes to and perceptions of high speed rail in the UK

With the planned expansion of high speed rail (HSR) in the UK, demand for longer-distance travel is expected to increase significantly over the coming decades. This paper presents a study into attitudes and perceptions of long distance travel in the UK, particularly in relation to HSR. A questionnaire was developed to investigate attitudes to travelling long distances and to HSR, importance of journey characteristics and current travel behaviours. A factor analysis of 46 attitude items yielded six factors: travel security, improvement to road and air, prestige of HSR, comfort, negative aspects of HSR and the usefulness of travel time. Analyses showed significant demographic and travel characteristic differences across the factors. There was also evidence of a more negative impact and lower prestige for people living closer to proposed HSR routes. Willingness to pay for travel time saved was related to a number of journey characteristics but the utility of time was also important. The findings are considered in light of theories of attitude change, attitudes to travel and sustainability and the implications for the future development of HSR policy, particularly in terms of balancing increased fares with utility of travel time

Bayesian inference for a spatio-temporal model of road traffic collision data

Improving road safety is hugely important with the number of deaths on the world’s roads remaining unacceptably high; an estimated 1.35 million people die each year (WHO, 2020). Current practice for treating collision hotspots is almost always reactive: once a threshold level of collisions has been exceeded during some predetermined observation period, treatment is applied (e.g. road safety cameras). However, more recently, methodology has been developed to predict collision counts at potential hotspots in future time periods, with a view to a more proactive treatment of road safety hotspots. Dynamic linear models provide a flexible framework for predicting collisions and thus enabling such a proactive treatment. In this paper, we demonstrate how such models can be used to capture both seasonal variability and spatial dependence in time dependent collision rates at several locations. The model allows for within- and out-of-sample forecasting for locations which are fully observed and for locations where some data are missing. We illustrate our approach using collision rate data from 8 Traffic Administration Zones in the US, and find that the model provides a good description of the underlying process and reasonable forecast accuracy

Using extreme value theory to evaluate the leading pedestrian interval road safety intervention

Improving road safety is hugely important with the number of deaths on the world's roads remaining unacceptably high; an estimated 1.3 million people die each year as a result of road traffic collisions. Current practice for treating collision hotspots is almost always reactive: once a threshold level of collisions has been overtopped during some pre‐determined observation period, treatment is applied (e.g., road safety cameras). Traffic collisions are rare, so prolonged observation periods are necessary. However, traffic conflicts are more frequent and are a margin of the social cost; hence, traffic conflict before/after studies can be conducted over shorter time periods. We investigate the effect of implementing the leading pedestrian interval treatment at signalised intersections as a safety intervention in a city in north America. Pedestrian‐vehicle traffic conflict data were collected from treatment and control sites during the before and after periods. We implement a before/after study on post‐encroachment times (PETs) where small PET values denote ‘near‐misses’. Hence, extreme value theory is employed to model extremes of our PET processes, with adjustments to the usual modelling framework to account for temporal dependence and treatment effects

Plastron respiration using commercial fabrics

A variety of insect and arachnid species are able to remain submerged in water indefinitely using plastron respiration. A plastron is a surface-retained film of air produced by surface morphology that acts as an oxygen-carbon dioxide exchange surface. Many highly water repellent and hydrophobic surfaces when placed in water exhibit a silvery sheen which is characteristic of a plastron. In this article, the hydrophobicity of a range of commercially available water repellent fabrics and polymer membranes is investigated, and how the surface of the materials mimics this mechanism of underwater respiration is demonstrated allowing direct extraction of oxygen from oxygenated water. The coverage of the surface with the plastron air layer was measured using confocal microscopy. A zinc/oxygen cell is used to consume oxygen within containers constructed from the different membranes, and the oxygen consumed by the cell is compared to the change in oxygen concentration as measured by an oxygen probe. By comparing the membranes to an air-tight reference sample, it was found that the membranes facilitated oxygen transfer from the water into the container, with the most successful membrane showing a 1.90:1 ratio between the cell oxygen consumption and the change in concentration within the container

Plastron properties of a superhydrophobic surface

Most insects and spiders drown when submerged during flooding or tidal inundation, but some are able to survive and others can remain submerged indefinitely without harm. Many achieve this by natural adaptations to their surface morphology to trap films of air, creating plastrons which fix the water-vapor interface and provide an incompressible oxygen-carbon dioxide exchange surface. Here the authors demonstrate how the surface of an extremely water-repellent foam mimics this mechanism of underwater respiration and allows direct extraction of oxygen from aerated water. The biomimetic principle demonstrated can be applied to a wide variety of man-made superhydrophobic materials