Existence of travelling wave solutions for a model of tumour invasion

The existence of travelling wave solutions to a haptotaxis dominated model is analysed. A version of this model has been derived in Perumpanani et al. (1999) to describe tumour invasion, where diffusion is neglected as it is assumed to play only a small role in the cell migration. By instead allowing diffusion to be small, we reformulate the model as a singular perturbation problem, which can then be analysed using geometric singular perturbation theory. We prove the existence of three types of physically realistic travelling wave solutions in the case of small diffusion. These solutions reduce to the no diffusion solutions in the singular limit as diffusion as is taken to zero. A fourth travelling wave solution is also shown to exist, but that is physically unrealistic as it has a component with negative cell population. The numerical stability, in particular the wavespeed of the travelling wave solutions is also discussed.

A geometric construction of travelling wave solutions to the Keller–Segel model

We study a version of the Keller–Segel model for bacterial chemotaxis, for which exact travelling wave solutions are explicitly known in the zero attractant diffusion limit. Using geometric singular perturbation theory, we construct travelling wave solutions in the small diffusion case that converge to these exact solutions in the singular limit.

Spatiotemporal patterns of Japanese Encephalitis in China, 2002–2010

OBJECTIVE The aim of the study is to examine the spatiotemporal pattern of Japanese Encephalitis (JE) in mainland China during 2002-2010. Specific objectives of the study were to quantify the temporal variation in incidence of JE cases, to determine if clustering of JE cases exists, to detect high risk spatiotemporal clusters of JE cases and to provide evidence-based preventive suggestions to relevant stakeholders. METHODS Monthly JE cases at the county level in mainland China during 2002-2010 were obtained from the China Information System for Diseases Control and Prevention (CISDCP). For the purpose of the analysis, JE case counts for nine years were aggregated into four temporal periods (2002; 2003-2005; 2006; and 2007-2010). Local Indicators of Spatial Association and spatial scan statistics were performed to detect and evaluate local high risk space-time clusters. RESULTS JE incidence showed a decreasing trend from 2002 to 2005 but peaked in 2006, then fluctuated over the study period. Spatial cluster analysis detected high value clusters, mainly located in Southwestern China. Similarly, we identified a primary spatiotemporal cluster of JE in Southwestern China between July and August, with the geographical range of JE transmission increasing over the past years. CONCLUSION JE in China is geographically clustered and its spatial extent dynamically changed during the last nine years in mainland China. This indicates that risk factors for JE infection are likely to be spatially heterogeneous. The results may assist national and local health authorities in the development/refinement of a better preventive strategy and increase the effectiveness of public health interventions against JE transmission.

Spatiotemporal patterns of Aedes aegyptipopulations in Cairns, Australia : assessing drivers of dengue transmission

OBJECTIVES To identify the meteorological drivers of dengue vector density and determine high- and low-risk transmission zones for dengue prevention and control in Cairns, Australia. METHODS Weekly adult female Ae. aegypti data were obtained from 79 double sticky ovitraps (SOs) located in Cairns for the period September 2007-May 2012. Maximum temperature, total rainfall and average relative humidity data were obtained from the Australian Bureau of Meteorology for the study period. Time series-distributed lag nonlinear models were used to assess the relationship between meteorological variables and vector density. Spatial autocorrelation was assessed via semivariography, and ordinary kriging was undertaken to predict vector density in Cairns. RESULTS Ae. aegypti density was associated with temperature and rainfall. However, these relationships differed between short (0-6 weeks) and long (0-30 weeks) lag periods. Semivariograms showed that vector distributions were spatially autocorrelated in September 2007-May 2008 and January 2009-May 2009, and vector density maps identified high transmission zones in the most populated parts of Cairns city, as well as Machans Beach. CONCLUSION Spatiotemporal patterns of Ae. aegypti in Cairns are complex, showing spatial autocorrelation and associations with temperature and rainfall. Sticky ovitraps should be placed no more than 1.2 km apart to ensure entomological coverage and efficient use of resources. Vector density maps provide evidence for the targeting of prevention and control activities. Further research is needed to explore the possibility of developing an early warning system of dengue based on meteorological and environmental factors.

Spatial Patterns of Malaria Reported Deaths in Yunnan Province, China

Malaria has been a heavy social and health burden in the remote and poor areas in southern China. Analyses of malaria epidemic patterns can uncover important features of malaria transmission. This study identified spatial clusters, seasonal patterns, and geographic variations of malaria deaths at a county level in Yunnan, China, during 1991–2010. A discrete Poisson model was used to identify purely spatial clusters of malaria deaths. Logistic regression analysis was performed to detect changes in geographic patterns. The results show that malaria mortality had declined in Yunnan over the study period and the most likely spatial clusters (relative risk [RR] = 23.03–32.06, P < 0.001) of malaria deaths were identified in western Yunnan along the China–Myanmar border. The highest risk of malaria deaths occurred in autumn (RR = 58.91, P < 0.001) and summer (RR = 31.91, P < 0.001). The results suggested that the geographic distribution of malaria deaths was significantly changed with longitude, which indicated there was decreased mortality of malaria in eastern areas over the last two decades, although there was no significant change in latitude during the same period. Public health interventions should target populations in western Yunnan along border areas, especially focusing on floating populations crossing international borders.

Did socio-ecological factors drive the spatiotemporal patterns of pandemic influenza A (H1N1)?

BACKGROUND Pandemic influenza A (H1N1) has a significant public health impact. This study aimed to examine the effect of socio-ecological factors on the transmission of H1N1 in Brisbane, Australia. METHODOLOGY We obtained data from Queensland Health on numbers of laboratory-confirmed daily H1N1 in Brisbane by statistical local areas (SLA) in 2009. Data on weather and socio-economic index were obtained from the Australian Bureau of Meteorology and the Australian Bureau of Statistics, respectively. A Bayesian spatial conditional autoregressive (CAR) model was used to quantify the relationship between variation of H1N1 and independent factors and to determine its spatiotemporal patterns. RESULTS Our results show that average increase in weekly H1N1 cases were 45.04% (95% credible interval (CrI): 42.63-47.43%) and 23.20% (95% CrI: 16.10-32.67%), for a 1 °C decrease in average weekly maximum temperature at a lag of one week and a 10mm decrease in average weekly rainfall at a lag of one week, respectively. An interactive effect between temperature and rainfall on H1N1 incidence was found (changes: 0.71%; 95% CrI: 0.48-0.98%). The auto-regression term was significantly associated with H1N1 transmission (changes: 2.5%; 95% CrI: 1.39-3.72). No significant association between socio-economic indexes for areas (SEIFA) and H1N1 was observed at SLA level. CONCLUSIONS Our results demonstrate that average weekly temperature at lag of one week and rainfall at lag of one week were substantially associated with H1N1 incidence at a SLA level. The ecological factors seemed to have played an important role in H1N1 transmission cycles in Brisbane, Australia.

Physical activity patterns and correlates among adults from a developing country : the Sri Lanka Diabetes and Cardiovascular Study

OBJECTIVE: To evaluate patterns of physical activity (PA), the prevalence of physical inactivity and the relationships between PA and sociodemographic, clinical and biochemical parameters among Sri Lankan adults. DESIGN: Descriptive cross-sectional study. SETTING: Nationally representative population-based survey conducted in Sri Lanka. SUBJECTS: Data on PA and associated details were obtained from 5000 adults. PA was assessed using the International Physical Activity Questionnaire (short-form). A binary logistic regression analysis was performed using the dichotomous variable ‘health-enhancing PA’ (05‘active’, 15‘inactive’). RESULTS: Sample size was 4485. Mean age was 46.1 (SD 15.1) years, 39.5% were males. The mean weekly total MET (metabolic equivalents of task) minutes of PA among the study population was 4703 (SD 4369). Males (5464 (SD 5452)) had a significantly higher weekly total MET minutes than females (4205 (SD 3394); P,0.001). Rural adults (5175 (SD 4583)) were significantly more active than urban adults (2956 (SD 2847); P<0.001). Tamils had the highest mean weekly total MET minutes among ethnicities. Those with tertiary education had lowest mean weekly total MET minutes. In all adults 60.0% were in the ‘highly active’ category, while only 11.0% were ‘inactive’ (males 14.6%, females 8.7%; P<0.001). Of the ‘highly active’ adults, 85.8% were residing in rural areas. Results of the binary logistic regression analysis indicated that female gender (OR52?1), age .70 years (OR53.8), urban living (OR52.5), Muslim ethnicity (OR52.7), tertiary education (OR53.6), obesity (OR51.8), diabetes (OR51.6), hypertension (OR51.2) and metabolic syndrome (OR51.3) were all associated with significantly increased odds of being physically ‘inactive’. CONCLUSIONS: The majority of Sri Lankan adults were ‘highly active’ physically. Female gender, older age, urban living, Muslim ethnicity and tertiary education were all significant predictors of physical inactivity. Physical inactivity was associated with obesity, diabetes, hypertension and metabolic syndrome.

Patterns of social capital associated with transit oriented development

In policy circles, transit oriented development (TOD) is believed to enhance social capital, however empirical evidence of this relationship is lacking. This research compares levels of social capital between TOD vs. non-TOD areas in Brisbane, Australia. Using a Two Step cluster analysis technique, three types of neighbourhood groupings were identified based on net employment density, net residential density, land use diversity, intersection density, and public transport accessibility: TODs, transit adjacent development (TADs) and traditional suburbs. Two dimensions of social capital were measured (trust and reciprocity, connections with neighbours) based on factor analysis of eight items representing elements of social capital. Multivariate regression analyses were conducted to identify links between the distributions of the dimensions of social capital on areas defined as TODs, TADs, and traditional suburbs controlling for socio-demographics and environmental factors. Results show that individuals living in TODs had a significantly higher level of trust and reciprocity and connections with neighbours compared with residents of TADs. It appears that TODs may foster the development of social sustainability.

Terrorism risk, resilience and volatility : a comparison of terrorism patterns in three Southeast Asian countries

Objective This article explores patterns of terrorist activity over the period from 2000 through 2010 across three target countries: Indonesia, the Philippines and Thailand. Methods We use self-exciting point process models to create interpretable and replicable metrics for three key terrorism concepts: risk, resilience and volatility, as defined in the context of terrorist activity. Results Analysis of the data shows significant and important differences in the risk, volatility and resilience metrics over time across the three countries. For the three countries analysed, we show that risk varied on a scale from 0.005 to 1.61 “expected terrorist attacks per day”, volatility ranged from 0.820 to 0.994 “additional attacks caused by each attack”, and resilience, as measured by the number of days until risk subsides to a pre-attack level, ranged from 19 to 39 days. We find that of the three countries, Indonesia had the lowest average risk and volatility, and the highest level of resilience, indicative of the relatively sporadic nature of terrorist activity in Indonesia. The high terrorism risk and low resilience in the Philippines was a function of the more intense, less clustered pattern of terrorism than what was evident in Indonesia. Conclusions Mathematical models hold great promise for creating replicable, reliable and interpretable “metrics” to key terrorism concepts such as risk, resilience and volatility.

Knitted images : drawing patterns

This Arts Based Education Research (Eisner 2008) work provides potent opportunity to consider different problems and challenges that impact on the progress of research (art as data making) and the theories being explored. It provides opportunity to transport ideas across between research activity, and teaching practices...

Damage evaluation based on a wave energy flow map using multiple PZT sensors

A new wave energy flow (WEF) map concept was proposed in this work. Based on it, an improved technique incorporating the laser scanning method and Betti’s reciprocal theorem was developed to evaluate the shape and size of damage as well as to realize visualization of wave propagation. In this technique, a simple signal processing algorithm was proposed to construct the WEF map when waves propagate through an inspection region, and multiple lead zirconate titanate (PZT) sensors were employed to improve inspection reliability. Various damages in aluminum and carbon fiber reinforced plastic laminated plates were experimentally and numerically evaluated to validate this technique. The results show that it can effectively evaluate the shape and size of damage from wave field variations around the damage in the WEF map.

Ship Motion Control : Course Keeping and Roll Stabilisation Using Rudder and Fins

Motion control systems have a significant impact on the performance of ships and marine structures allowing them to perform tasks in severe sea states and during long periods of time. Ships are designed to operate with adequate reliability and economy, and in order to achieve this, it is essential to control the motion. For each type of ship and operation performed (transit, landing a helicopter, fishing, deploying and recovering loads, etc.), there are not only desired motion settings, but also limits on the acceptable (undesired) motion induced by the environment. The task of a ship motion control system is therefore to act on the ship so it follows the desired motion as closely as possible. This book provides an introduction to the field of ship motion control by studying the control system designs for course-keeping autopilots with rudder roll stabilisation and integrated rudder-fin roll stabilisation. These particular designs provide a good overview of the difficulties encountered by designers of ship motion control systems and, therefore, serve well as an example driven introduction to the field. The idea of combining the control design of autopilots with that of fin roll stabilisers, and the idea of using rudder induced roll motion as a sole source of roll stabilisation seems to have emerged in the late 1960s. Since that time, these control designs have been the subject of continuous and ongoing research. This ongoing interest is a consequence of the significant bearing that the control strategy has on the performance and the issues associated with control system design. The challenges of these designs lie in devising a control strategy to address the following issues: underactuation, disturbance rejection with a non minimum phase system, input and output constraints, model uncertainty, and large unmeasured stochastic disturbances. To date, the majority of the work reported in the literature has focused strongly on some of the design issues whereas the remaining issues have been addressed using ad hoc approaches. This has provided an additional motivation for revisiting these control designs and looking at the benefits of applying a contemporary design framework, which can potentially address the majority of the design issues.

Kalman filtering for positioning and heading control of ships and offshore rigs

In this article, we have described the main components of a ship motion-control system and two particular motion-control problems that require wave filtering, namely, dynamic positioning and heading autopilot. Then, we discussed the models commonly used for vessel response and showed how these models are used for Kalman filter design. We also briefly discussed parameter and noise covariance estimation, which are used for filter tuning. To illustrate the performance, a case study based on numerical simulations for a ship autopilot was considered. The material discussed in this article conforms to modern commercially available ship motion-control systems. Most of the vessels operating in the offshore industry worldwide use Kalman filters for velocity estimation and wave filtering. Thus, the article provides an up-to-date tutorial and overview of Kalman-filter-based wave filtering.

Constrained predictive control of ship fin stabilizers to prevent dynamic stall

In moderate to high sea states, the effectiveness of ship fin stabilizers can severely deteriorate due to nonlinear effects arising from unsteady hydrodynamic characteristics of the fins: dynamic stall. These nonlinear effects take the form of a hysteresis, and they become very significant when the effective angle of attack of the fins exceeds a certain threshold angle. Dynamic stall can result in a complete loss of control action depending on how much the fins exceed the threshold angle. When this is detected, it is common to reduce the gain of the controller that commands the fins. This approach is cautious and tends to reduce performance when the conditions leading to dynamic stall disappear. An alternative approach for preventing the effects while keeping high performance, consists of estimating the effective angle of attack and set a conservative constraint on it as part of the control objectives. In this paper, we investigate the latter approach, and propose the use of a model predictive control (MPC) to prevent the development of these nonlinear effects by considering constraints on both the mechanical angle of the fins and the effective angle of attack.