Incorporating spatial correlations into multispecies mean-field models

In biology, we frequently observe different species existing within the same environment. For example, there are many cell types in a tumour, or different animal species may occupy a given habitat. In modelling interactions between such species, we often make use of the mean field approximation, whereby spatial correlations between the locations of individuals are neglected. Whilst this approximation holds in certain situations, this is not always the case, and care must be taken to ensure the mean field approximation is only used in appropriate settings. In circumstances where the mean field approximation is unsuitable we need to include information on the spatial distributions of individuals, which is not a simple task. In this paper we provide a method that overcomes many of the failures of the mean field approximation for an on-lattice volume-excluding birth-death-movement process with multiple species. We explicitly take into account spatial information on the distribution of individuals by including partial differential equation descriptions of lattice site occupancy correlations. We demonstrate how to derive these equations for the multi-species case, and show results specific to a two-species problem. We compare averaged discrete results to both the mean field approximation and our improved method which incorporates spatial correlations. We note that the mean field approximation fails dramatically in some cases, predicting very different behaviour from that seen upon averaging multiple realisations of the discrete system. In contrast, our improved method provides excellent agreement with the averaged discrete behaviour in all cases, thus providing a more reliable modelling framework. Furthermore, our method is tractable as the resulting partial differential equations can be solved efficiently using standard numerical techniques.

First flush behaviour in urban residential catchments

The current state of knowledge in relation to first flush does not provide a clear understanding of the role of rainfall and catchment characteristics in influencing this phenomenon. This is attributed to the inconsistent findings from research studies due to the unsatisfactory selection of first flush indicators and how first flush is defined. The research study discussed in this thesis provides the outcomes of a comprehensive analysis on the influence of rainfall and catchment characteristics on first flush behaviour in residential catchments. Two sets of first flush indicators are introduced in this study. These indicators were selected such that they are representative in explaining in a systematic manner the characteristics associated with first flush. Stormwater samples and rainfall-runoff data were collected and recorded from stormwater monitoring stations established at three urban catchments at Coomera Waters, Gold Coast, Australia. In addition, historical data were also used to support the data analysis. Three water quality parameters were analysed, namely, total suspended solids (TSS), total phosphorus (TP) and total nitrogen (TN). The data analyses were primarily undertaken using multi criteria decision making methods, PROMETHEE and GAIA. Based on the data obtained, the pollutant load distribution curve (LV) was determined for the individual rainfall events and pollutant types. Accordingly, two sets of first flush indicators were derived from the curve, namely, cumulative load wash-off for every 10% of runoff volume interval (interval first flush indicators or LV) from the beginning of the event and the actual pollutant load wash-off during a 10% increment in runoff volume (section first flush indicators or P). First flush behaviour showed significant variation with pollutant types. TSS and TP showed consistent first flush behaviour. However, the dissolved fraction of TN showed significant differences to TSS and TP first flush while particulate TN showed similarities. Wash-off of TSS, TP and particulate TN during the first 10% of the runoff volume showed no influence from corresponding rainfall intensity. This was attributed to the wash-off of weakly adhered solids on the catchment surface referred to as "short term pollutants" or "weakly adhered solids" load. However, wash-off after 10% of the runoff volume showed dependency on the rainfall intensity. This is attributed to the wash-off of strongly adhered solids being exposed when the weakly adhered solids diminish. The wash-off process was also found to depend on rainfall depth at the end part of the event as the strongly adhered solids are loosened due to impact of rainfall in the earlier part of the event. Events with high intensity rainfall bursts after 70% of the runoff volume did not demonstrate first flush behaviour. This suggests that rainfall pattern plays a critical role in the occurrence of first flush. Rainfall intensity (with respect to the rest of the event) that produces 10% to 20% runoff volume play an important role in defining the magnitude of the first flush. Events can demonstrate high magnitude first flush when the rainfall intensity occurring between 10% and 20% of the runoff volume is comparatively high while low rainfall intensities during this period produces low magnitude first flush. For events with first flush, the phenomenon is clearly visible up to 40% of the runoff volume. This contradicts the common definition that first flush only exists, if for example, 80% of the pollutant mass is transported in the first 30% of runoff volume. First flush behaviour for TN is different compared to TSS and TP. Apart from rainfall characteristics, the composition and the availability of TN on the catchment also play an important role in first flush. The analysis confirmed that events with low rainfall intensity can produce high magnitude first flush for the dissolved fraction of TN, while high rainfall intensity produce low dissolved TN first flush. This is attributed to the source limiting behaviour of dissolved TN wash-off where there is high wash-off during the initial part of a rainfall event irrespective of the intensity. However, for particulate TN, the influence of rainfall intensity on first flush characteristics is similar to TSS and TP. The data analysis also confirmed that first flush can occur as high magnitude first flush, low magnitude first flush or non existence of first flush. Investigation of the influence of catchment characteristics on first flush found that the key factors that influence the phenomenon are the location of the pollutant source, spatial distribution of the pervious and impervious surfaces in the catchment, drainage network layout and slope of the catchment. This confirms that first flush phenomenon cannot be evaluated based on a single or a limited set of parameters as a number of catchment characteristics should be taken into account. Catchments where the pollutant source is located close to the outlet, a high fraction of road surfaces, short travel time to the outlet, with steep slopes can produce high wash-off load during the first 50% of the runoff volume. Rainfall characteristics have a comparatively dominant impact on the wash-off process compared to the catchment characteristics. In addition, the pollutant characteristics also should be taken into account in designing stormwater treatment systems due to different wash-off behaviour. Analysis outcomes confirmed that there is a high TSS load during the first 20% of the runoff volume followed by TN which can extend up to 30% of the runoff volume. In contrast, high TP load can exist during the initial and at the end part of a rainfall event. This is related to the composition of TP available for the wash-off.

Agreement between temporal and spatial gait parameters from an instrumented walkway and treadmill system at matched walking speed

Background Commercially available instrumented treadmill systems that provide continuous measures of temporospatial gait parameters have recently become available for clinical gait analysis. This study evaluated the level of agreement between temporospatial gait parameters derived from a new instrumented treadmill, which incorporated a capacitance-based pressure array, with those measured by a conventional instrumented walkway (criterion standard). Methods Temporospatial gait parameters were estimated from 39 healthy adults while walking over an instrumented walkway (GAITRite®) and instrumented treadmill system (Zebris) at matched speed. Differences in temporospatial parameters derived from the two systems were evaluated using repeated measures ANOVA models. Pearson-product-moment correlations were used to investigate relationships between variables measured by each system. Agreement was assessed by calculating the bias and 95% limits of agreement. Results All temporospatial parameters measured via the instrumented walkway were significantly different from those obtained from the instrumented treadmill (P < .01). Temporospatial parameters derived from the two systems were highly correlated (r, 0.79–0.95). The 95% limits of agreement for temporal parameters were typically less than ±2% of gait cycle duration. However, 95% limits of agreement for spatial measures were as much as ±5 cm. Conclusions Differences in temporospatial parameters between systems were small but statistically significant and of similar magnitude to changes reported between shod and unshod gait in healthy young adults. Temporospatial parameters derived from an instrumented treadmill, therefore, are not representative of those obtained from an instrumented walkway and should not be interpreted with reference to literature on overground walking.

Multiple types of data are required to identify the mechanisms influencing the spatial expansion of melanoma cell colonies

Background The expansion of cell colonies is driven by a delicate balance of several mechanisms including cell motility, cell-to-cell adhesion and cell proliferation. New approaches that can be used to independently identify and quantify the role of each mechanism will help us understand how each mechanism contributes to the expansion process. Standard mathematical modelling approaches to describe such cell colony expansion typically neglect cell-to-cell adhesion, despite the fact that cell-to-cell adhesion is thought to play an important role. Results We use a combined experimental and mathematical modelling approach to determine the cell diffusivity, D, cell-to-cell adhesion strength, q, and cell proliferation rate, ?, in an expanding colony of MM127 melanoma cells. Using a circular barrier assay, we extract several types of experimental data and use a mathematical model to independently estimate D, q and ?. In our first set of experiments, we suppress cell proliferation and analyse three different types of data to estimate D and q. We find that standard types of data, such as the area enclosed by the leading edge of the expanding colony and more detailed cell density profiles throughout the expanding colony, does not provide sufficient information to uniquely identify D and q. We find that additional data relating to the degree of cell-to-cell clustering is required to provide independent estimates of q, and in turn D. In our second set of experiments, where proliferation is not suppressed, we use data describing temporal changes in cell density to determine the cell proliferation rate. In summary, we find that our experiments are best described using the range D = 161 - 243 ?m2 hour-1, q = 0.3 - 0.5 (low to moderate strength) and ? = 0.0305 - 0.0398 hour-1, and with these parameters we can accurately predict the temporal variations in the spatial extent and cell density profile throughout the expanding melanoma cell colony. Conclusions Our systematic approach to identify the cell diffusivity, cell-to-cell adhesion strength and cell proliferation rate highlights the importance of integrating multiple types of data to accurately quantify the factors influencing the spatial expansion of melanoma cell colonies.

The impact of spatial scales and spatial smoothing on the outcome of Bayesian spatial model

Discretization of a geographical region is quite common in spatial analysis. There have been few studies into the impact of different geographical scales on the outcome of spatial models for different spatial patterns. This study aims to investigate the impact of spatial scales and spatial smoothing on the outcomes of modelling spatial point-based data. Given a spatial point-based dataset (such as occurrence of a disease), we study the geographical variation of residual disease risk using regular grid cells. The individual disease risk is modelled using a logistic model with the inclusion of spatially unstructured and/or spatially structured random effects. Three spatial smoothness priors for the spatially structured component are employed in modelling, namely an intrinsic Gaussian Markov random field, a second-order random walk on a lattice, and a Gaussian field with Matern correlation function. We investigate how changes in grid cell size affect model outcomes under different spatial structures and different smoothness priors for the spatial component. A realistic example (the Humberside data) is analyzed and a simulation study is described. Bayesian computation is carried out using an integrated nested Laplace approximation. The results suggest that the performance and predictive capacity of the spatial models improve as the grid cell size decreases for certain spatial structures. It also appears that different spatial smoothness priors should be applied for different patterns of point data.

Assessing land-use and transport integration via a spatial composite indexing model

Achieving sustainable urban development is identified as one ultimate goal of many contemporary planning endeavours and has become central to formulation of urban planning policies. Within this concept, land-use and transport integration is highlighted as one of the most important and attainable policy objectives. In many cities, integration is embraced as an integral part of local development plans, and a number of key integration principles are identified. However, the lack of available evaluation methods to measure extent of urban sustainability levels prevents successful implementation of these principles. This paper introduces a new indicator-based spatial composite indexing model developed to measure sustainability performance of urban settings by taking into account land-use and transport integration principles. Model indicators are chosen via a thorough selection process in line with key principles of land-use and transport integration. These indicators are grouped into categories and themes according to their topical relevance. These indicators are then aggregated to form a spatial composite index to portray an overview of the sustainability performance of the pilot study area used for model demonstration. The study results revealed that the model is a practical instrument for evaluating success of local integration policies and visualizing sustainability performance of built environments and useful in both identifying problematic areas as well as formulating policy interventions.

Towards bio-inspired place recognition over multiple spatial scales

This paper presents a new multi-scale place recognition system inspired by the recent discovery of overlapping, multi-scale spatial maps stored in the rodent brain. By training a set of Support Vector Machines to recognize places at varying levels of spatial specificity, we are able to validate spatially specific place recognition hypotheses against broader place recognition hypotheses without sacrificing localization accuracy. We evaluate the system in a range of experiments using cameras mounted on a motorbike and a human in two different environments. At 100% precision, the multiscale approach results in a 56% average improvement in recall rate across both datasets. We analyse the results and then discuss future work that may lead to improvements in both robotic mapping and our understanding of sensory processing and encoding in the mammalian brain.

Spatial analysis of community-onset Staphylococcus aureus bacteremia in Queensland, Australia

OBJECTIVES To investigate and describe the relationship between indigenous Australian populations, residential aged care services, and community-onset Staphylococcus aureus bacteremia (SAB) among patients admitted to public hospitals in Queensland, Australia. DESIGN Ecological study. METHODS We used administrative healthcare data linked to microbiology results from patients with SAB admitted to Queensland public hospitals from 2005 through 2010 to identify community-onset infections. Data about indigenous Australian population and residential aged care services at the local government area level were obtained from the Queensland Office of Economic and Statistical Research. Associations between community-onset SAB and indigenous Australian population and residential aged care services were calculated using Poisson regression models in a Bayesian framework. Choropleth maps were used to describe the spatial patterns of SAB risk. RESULTS We observed a 21% increase in relative risk (RR) of bacteremia with methicillin-susceptible S. aureus (MSSA; RR, 1.21 [95% credible interval, 1.15-1.26]) and a 24% increase in RR with nonmultiresistant methicillin-resistant S. aureus (nmMRSA; RR, 1.24 [95% credible interval, 1.13-1.34]) with a 10% increase in the indigenous Australian population proportion. There was no significant association between RR of SAB and the number of residential aged care services. Areas with the highest RR for nmMRSA and MSSA bacteremia were identified in the northern and western regions of Queensland. CONCLUSIONS The RR of community-onset SAB varied spatially across Queensland. There was increased RR of community-onset SAB with nmMRSA and MSSA in areas of Queensland with increased indigenous population proportions. Additional research should be undertaken to understand other factors that increase the risk of infection due to this organism.

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.

Neoliberalism and Spatial Adaptation

Human spatial environments must adapt to climate change. Spatial planning is central to climate change adaptation and potentially well suited to the task, however neoliberal influences and trends threaten this capacity. This paper explores the significance of neoliberal influences on urban planning to climate change adaptation. The potential form of spatial adaptation within the context of a planning environment influenced by neoliberal principles is evaluated. This influence relates to spatial scale, temporal scale, responsibility for action, strategies and mechanisms, accrual of benefits, negotiation of priorities and approach to uncertainty. This paper presents a conceptual framework of the influence of neoliberalism on spatial adaptation. It identifies the potential characteristics, challenges and opportunities of spatial adaptation under a neoliberal frame. The neoliberal frame does not entirely preclude spatial adaptation but significantly influence its form. Neoliberal approaches involve individual action in response to private incentives and near term impacts while collective action, regulatory mechanisms and long term planning is approached cautiously. Challenges concern the degree to which collective action and a long term orientation are necessary, how individual adaptation relates to collective vulnerability and the prioritisation of adaptation by markets. Opportunities might involve the operability of individual and local adaptation, the existence of private incentives to adapt and the potential to align adaptation with entrepreneurial projects.

Spatial and developmental heterogeneity of calcium signaling in olfactory ensheathing cells

Olfactory ensheathing cells (OECs) are specialized glial cells in the mammalian olfactory system supporting growth of axons from the olfactory epithelium into the olfactory bulb. OECs in the olfactory bulb can be subdivided into OECs of the outer nerve layer and the inner nerve layer according to the expression of marker proteins and their location in the nerve layer. In the present study, we have used confocal calcium imaging of OECs in acute mouse brain slices and olfactory bulbs in toto to investigate physiological differences between OEC subpopulations. OECs in the outer nerve layer, but not the inner nerve layer, responded to glutamate, ATP, serotonin, dopamine, carbachol, and phenylephrine with increases in the cytosolic calcium concentration. The calcium responses consisted of a transient and a tonic component, the latter being mediated by store-operated calcium entry. Calcium measurements in OECs during the first three postnatal weeks revealed a downregulation of mGluR(1) and P2Y(1) receptor-mediated calcium signaling within the first 2 weeks, suggesting that the expression of these receptors is developmentally controlled. In addition, electrical stimulation of sensory axons evoked calcium signaling via mGluR(1) and P2Y(1) only in outer nerve layer OECs. Downregulation of the receptor-mediated calcium responses in postnatal animals is reflected by a decrease in amplitude of stimulation-evoked calcium transients in OECs from postnatal days 3 to 21. In summary, the results presented reveal striking differences in receptor responses during development and in axon-OEC communication between the two subpopulations of OECs in the olfactory bulb.

Visualization of predictive distributions for discrete spatial-temporal log Cox processes approximated with MCMC

An important aspect of decision support systems involves applying sophisticated and flexible statistical models to real datasets and communicating these results to decision makers in interpretable ways. An important class of problem is the modelling of incidence such as fire, disease etc. Models of incidence known as point processes or Cox processes are particularly challenging as they are ‘doubly stochastic’ i.e. obtaining the probability mass function of incidents requires two integrals to be evaluated. Existing approaches to the problem either use simple models that obtain predictions using plug-in point estimates and do not distinguish between Cox processes and density estimation but do use sophisticated 3D visualization for interpretation. Alternatively other work employs sophisticated non-parametric Bayesian Cox process models, but do not use visualization to render interpretable complex spatial temporal forecasts. The contribution here is to fill this gap by inferring predictive distributions of Gaussian-log Cox processes and rendering them using state of the art 3D visualization techniques. This requires performing inference on an approximation of the model on a discretized grid of large scale and adapting an existing spatial-diurnal kernel to the log Gaussian Cox process context.

A stochastic neighborhood conditional autoregressive model for spatial data

A spatial process observed over a lattice or a set of irregular regions is usually modeled using a conditionally autoregressive (CAR) model. The neighborhoods within a CAR model are generally formed deterministically using the inter-distances or boundaries between the regions. An extension of CAR model is proposed in this article where the selection of the neighborhood depends on unknown parameter(s). This extension is called a Stochastic Neighborhood CAR (SNCAR) model. The resulting model shows flexibility in accurately estimating covariance structures for data generated from a variety of spatial covariance models. Specific examples are illustrated using data generated from some common spatial covariance functions as well as real data concerning radioactive contamination of the soil in Switzerland after the Chernobyl accident.

Nurse-led chest drain removal in a cardiac high dependency unit

Within the cardiac high dependency unit it is currently a member of the surgical team who makes the decision for a patient's chest drain to be removed after cardiac surgery. This has often resulted in delays in discharging one patient and therefore in admitting the next. A pilot study was carried out using a working standard that had been developed, incorporating an algorithmic model. The results have enabled nursing staff in a cardiac high dependency unit to undertake this responsibility independently.

A spatial-indexing model for measuring neighbourhood-level land-use and transport integration

Significant attention has been given in urban policy literature to the integration of land-use and transport planning and policies—with a view to curbing sprawling urban form and diminishing externalities associated with car-dependent travel patterns. By taking land-use and transport interaction into account, this debate mainly focuses on how a successful integration can contribute to societal well-being, providing efficient and balanced economic growth while accomplishing the goal of developing sustainable urban environments and communities. The integration is also a focal theme of contemporary urban development models, such as smart growth, liveable neighbourhoods, and new urbanism. Even though available planning policy options for ameliorating urban form and transport-related externalities have matured—owing to growing research and practice worldwide—there remains a lack of suitable evaluation models to reflect on the current status of urban form and travel problems or on the success of implemented integration policies. In this study we explore the applicability of indicator-based spatial indexing to assess land-use and transport integration at the neighbourhood level. For this, a spatial index is developed by a number of indicators compiled from international studies and trialled in Gold Coast, Queensland, Australia. The results of this modelling study reveal that it is possible to propose an effective metric to determine the success level of city plans considering their sustainability performance via composite indicator methodology. The model proved useful in demarcating areas where planning intervention is applicable, and in identifying the most suitable locations for future urban development and plan amendments. Lastly, we integrate variance-based sensitivity analysis with the spatial indexing method, and discuss the applicability of the model in other urban contexts.