On the spread of epidemics in a closed heterogeneous population

Heterogeneity is an important property of any population experiencing a disease. Here we apply general methods of the theory of heterogeneous populations to the simplest mathematical models in epidemiology. In particular, an SIR (susceptible-infective-removed) model is formulated and analyzed for different sources of heterogeneity. It is shown that a heterogeneous model can be reduced to a homogeneous model with a nonlinear transmission function, which is given in explicit form. The widely used power transmission function is deduced from a heterogeneous model with the initial gamma-distribution of the disease parameters. Therefore, a mechanistic derivation of the phenomenological model, which mimics reality very well, is provided. The equation for the final size of an epidemic for an arbitrary initial distribution is found. The implications of population heterogeneity are discussed, in particular, it is pointed out that usual moment-closure methods can lead to erroneous conclusions if applied for the study of the long-term behavior of the model.Comment: 23 pages, 2 figure

Axioms for higher torsion invariants of smooth bundles

We explain the relationship between various characteristic classes for smooth manifold bundles known as ``higher torsion'' classes. We isolate two fundamental properties that these cohomology classes may or may not have: additivity and transfer. We show that higher Franz-Reidemeister torsion and higher Miller-Morita-Mumford classes satisfy these axioms. Conversely, any characteristic class of smooth bundles satisfying the two axioms must be a linear combination of these two examples. We also show how higher torsion invariants can be computed using only the axioms. Finally, we explain the conjectured formula of S. Goette relating higher analytic torsion classes and higher Franz-Reidemeister torsion.Comment: 24 pages, 0 figure

The validity and reliability of the exposure index as a metric for estimating the radiation dose to the patient

Introduction With the introduction of digital radiography, the feedback between image quality and over-exposure has been partly lost which in some cases has led to a steady increase in dose. Over the years the introduction of exposure index (EI) has been used to resolve this phenomenon referred to as ‘dose creep’. Even though EI is often vendor specific it is always a related of the radiation exposure to the detector. Due to the nature of this relationship EI can also be used as a patient dose indicator, however this is not widely investigated in literature. Methods A total of 420 dose-area-product (DAP) and EI measurements were taken whilst varying kVp, mAs and body habitus on two different anthropomorphic phantoms (pelvis and chest). Using linear regression, the correlation between EI and DAP were examined. Additionally, two separate region of interest (ROI) placements/per phantom where examined in order to research any effect on EI. Results When dividing the data into subsets, a strong correlation between EI and DAP was shown with all R-squared values > 0.987. Comparison between the ROI placements showed a significant difference between EIs for both placements. Conclusion This research shows a clear relationship between EI and radiation dose which is dependent on a wide variety of factors such as ROI placement, body habitus. In addition, pathology and manufacturer specific EI’s are likely to be of influence as well. Implications for practice The combination of DAP and EI might be used as a patient dose indicator. However, the influencing factors as mentioned in the conclusion should be considered and examined before implementation

Robot mapping and localisation in metal water pipes using hydrophone induced vibration and map alignment by dynamic time warping

Water is a highly valuable resource so asset management of associated infrastructure is of critical importance. Water distribution pipe networks are usually buried, and so are difficult to access. Robots are therefore appealing for performing inspection and detecting damage to target repairs. However, robot mapping and localisation of buried water pipes has not been widely investigated to date, and is challenging because pipes tend to be relatively featureless. In this paper we propose a mapping and localisation algorithm for metal water pipes with two key novelties: the development of a new type of map based on hydrophone induced vibration signals of metal pipes, and a mapping algorithm based on spatial warping and averaging of dead reckoning signals used to calibrate the map (using dynamic time warping). Localisation is performed using both terrain-based extended Kalman filtering and also particle filtering. We successfully demonstrate and evaluate the approach on a combination of experimental and simulation data, showing improved localisation compared to dead reckoning

Friction and wear of Cu-15 wt%Ni-8 wt%Sn bronze lubricated by grease at room and elevated temperature

Cu-15 wt%Ni-8 wt%Sn (CuNiSn) bronze alloy shows promising bearing performance when used in tribological applications and has attracted increasing research interest. In this work, the tribological performance of CuNiSn in terms of friction and wear were investigated in a ball-on-disc contact configuration, sliding against a Al2O3 ball under varying normal loads (1 and 4 N) and environmental temperatures (room temperature (~18 °C) and 110 °C). Post-test characterization techniques, including optical profilometry, scanning electron microscopy (SEM), energy dispersive X-ray (EDX) and transmission electron microscopy (TEM) were adopted to characterize the wear track on the CuNiSn surface after 13,500 cycles of reciprocating sliding. Both friction and wear behaviour was found to depend on the load and temperature whilst wear resistance reduced with increased temperature. A mechanically mixed layer (MML) and plastic deformation layer (PDL) were characterized by TEM micrographs of the cross-section from the wear track. Under 4 N load, a 1–1.5 μm thick tribolayer was developed during sliding at room temperature compared with a 200–300 nm tribolayer at 110 °C. The friction and wear mechanisms were largely dominated by properties of the tribolayers which were initially associated with and affected by load and temperature

PipeSLAM: Simultaneous Localisation and Mapping in Feature Sparse Water Pipes using the Rao-Blackwellised Particle Filter

Water, a valuable resource, is usually distributed through urban environments by buried pipes. These pipes are difficult to access for inspection, maintenance and repair. This makes in-pipe robots an appealing technology for inspecting water pipes and localising damage prior to repair from above ground. Accurate localisation of damage is of critical importance because of the costs associated with excavating roads, disrupting traffic and disrupting the water supply. The problem is that pipes tend to be relatively featureless making robot localisation a challenging problem. In this paper we propose a novel simultaneous localisation and mapping (SLAM) algorithm for metal water pipes. The approach we take is to excite pipe vibration with a hydrophone (sound induced vibration), which leads to a map of pipe vibration amplitude over space. We then develop a SLAM algorithm that makes use of this new type of map, where the estimation method is based on the Rao-Blackwellised particle filter (RBPF), termed PipeSLAM. The approach is also suited to SLAM in plastic water pipes using a similar type of map derived from ultrasonic sensing. We successfully demonstrate the feasibility of the approach using a combination of experimental and simulation data

Robot localization in water pipes using acoustic signals and pose graph optimization

One of the most fundamental tasks for robots inspecting water distribution pipes is localization, which allows for autonomous navigation, for faults to be communicated, and for interventions to be instigated. Pose-graph optimization using spatially varying information is used to enable localization within a feature-sparse length of pipe. We present a novel method for improving estimation of a robot’s trajectory using the measured acoustic field, which is applicable to other measurements such as magnetic field sensing. Experimental results show that the use of acoustic information in pose-graph optimization reduces errors by 39% compared to the use of typical pose-graph optimization using landmark features only. High location accuracy is essential to efficiently and effectively target investment to maximise the use of our aging pipe infrastructure

Tribological behaviour of self-lubricating Mg matrix composites reinforced with silicon carbide and tungsten disulfide

In this study, magnesium matrix composites reinforced with 5 wt% WS2 and 15–20 wt% SiC particles were sintered via powder processing. The friction and wear behaviour were studied using a ball-on-disc tribometer against Al2O3 ball, subjected to normal loads of 1–4 N, room temperature and 110 °C, sliding speed of 22.5 mm/s, and lubricant of PAO base oil. The wear track and tribo-layer generated were investigated by optical profilometry and scanning electron microscopy. The average friction coefficient for Mg metal matrix composites (MMCs) was found to be 0.1–0.2 compared with 0.16–0.46 for pure Mg. Under all testing conditions, the Mg MMCs exhibited much lower friction coefficient and outstanding anti-wear property compared with unreinforced Mg and the Mg alloy AZ31