Distinguishing between mean-field, moment dynamics and stochastic descriptions of birth-death-movement processes

Mathematical descriptions of birth–death–movement processes are often calibrated to measurements from cell biology experiments to quantify tissue growth rates. Here we describe and analyze a discrete model of a birth–death-movement process applied to a typical two–dimensional cell biology experiment. We present three different descriptions of the system: (i) a standard mean–field description which neglects correlation effects and clustering; (ii) a moment dynamics description which approximately incorporates correlation and clustering effects, and; (iii) averaged data from repeated discrete simulations which directly incorporates correlation and clustering effects. Comparing these three descriptions indicates that the mean–field and moment dynamics approaches are valid only for certain parameter regimes, and that both these descriptions fail to make accurate predictions of the system for sufficiently fast birth and death rates where the effects of spatial correlations and clustering are sufficiently strong. Without any method to distinguish between the parameter regimes where these three descriptions are valid, it is possible that either the mean–field or moment dynamics model could be calibrated to experimental data under inappropriate conditions, leading to errors in parameter estimation. In this work we demonstrate that a simple measurement of agent clustering and correlation, based on coordination number data, provides an indirect measure of agent correlation and clustering effects, and can therefore be used to make a distinction between the validity of the different descriptions of the birth–death–movement process.

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.

Back to the roots : mean-variance analysis of relevance estimations

Recently, mean-variance analysis has been proposed as a novel paradigm to model document ranking in Information Retrieval. The main merit of this approach is that it diversifies the ranking of retrieved documents. In its original formulation, the strategy considers both the mean of relevance estimates of retrieved documents and their variance. How- ever, when this strategy has been empirically instantiated, the concepts of mean and variance are discarded in favour of a point-wise estimation of relevance (to replace the mean) and of a parameter to be tuned or, alternatively, a quantity dependent upon the document length (to replace the variance). In this paper we revisit this ranking strategy by going back to its roots: mean and variance. For each retrieved document, we infer a relevance distribution from a series of point-wise relevance estimations provided by a number of different systems. This is used to compute the mean and the variance of document relevance estimates. On the TREC Clueweb collection, we show that this approach improves the retrieval performances. This development could lead to new strategies to address the fusion of relevance estimates provided by different systems.

Estimating present day extreme water level exceedance probabilities around the coastline of Australia : tides, extra-tropical storm surges and mean sea level

The occurrence of extreme water levels along low-lying, highly populated and/or developed coastlines can lead to considerable loss of life and billions of dollars of damage to coastal infrastructure. Therefore it is vitally important that the exceedance probabilities of extreme water levels are accurately evaluated to inform risk-based flood management, engineering and future land-use planning. This ensures the risk of catastrophic structural failures due to under-design or expensive wastes due to over-design are minimised. This paper estimates for the first time present day extreme water level exceedence probabilities around the whole coastline of Australia. A high-resolution depth averaged hydrodynamic model has been configured for the Australian continental shelf region and has been forced with tidal levels from a global tidal model and meteorological fields from a global reanalysis to generate a 61-year hindcast of water levels. Output from this model has been successfully validated against measurements from 30 tide gauge sites. At each numeric coastal grid point, extreme value distributions have been fitted to the derived time series of annual maxima and the several largest water levels each year to estimate exceedence probabilities. This provides a reliable estimate of water level probabilities around southern Australia; a region mainly impacted by extra-tropical cyclones. However, as the meteorological forcing used only weakly includes the effects of tropical cyclones, extreme water level probabilities are underestimated around the western, northern and north-eastern Australian coastline. In a companion paper we build on the work presented here and more accurately include tropical cyclone-induced surges in the estimation of extreme water level. The multi-decadal hindcast generated here has been used primarily to estimate extreme water level exceedance probabilities but could be used more widely in the future for a variety of other research and practical applications.

What does it mean to 'securitize' infectious diseases?

This paper seeks to explain how the selective securitization of infectious disease arose, and to analyze the policy successes from this move. It is argued that despite some success, such as the revised International Health Regulations (IHR) in 2005, there remain serious deficiencies in the political outputs from the securitization of infectious disease.

Interacting motile agents : taking a mean-field approach beyond monomers and nearest-neighbor steps

We consider a discrete agent-based model on a one-dimensional lattice, where each agent occupies L sites and attempts movements over a distance of d lattice sites. Agents obey a strict simple exclusion rule. A discrete-time master equation is derived using a mean-field approximation and careful probability arguments. In the continuum limit, nonlinear diffusion equations that describe the average agent occupancy are obtained. Averaged discrete simulation data are generated and shown to compare very well with the solution to the derived nonlinear diffusion equations. This framework allows us to approach a lattice-free result using all the advantages of lattice methods. Since different cell types have different shapes and speeds of movement, this work offers insight into population-level behavior of collective cellular motion.

Estimating the mean critical gap

The estimation of the critical gap has been an issue since the 1970s, when gap acceptance was introduced to evaluate the capacity of unsignalized intersections. The critical gap is the shortest gap that a driver is assumed to accept. A driver’s critical gap cannot be measured directly and a number of techniques have been developed to estimate the mean critical gaps of a sample of drivers. This paper reviews the ability of the Maximum Likelihood technique and the Probability Equilibrium Method to predict the mean and standard deviation of the critical gap with a simulation of 100 drivers, repeated 100 times for each flow condition. The Maximum Likelihood method gave consistent and unbiased estimates of the mean critical gap. Whereas the probability equilibrium method had a significant bias that was dependent on the flow in the priority stream. Both methods were reasonably consistent, although the Maximum Likelihood Method was slightly better. If drivers are inconsistent, then again the Maximum Likelihood method is superior. A criticism levelled at the Maximum Likelihood method is that a distribution of the critical gap has to be assumed. It was shown that this does not significantly affect its ability to predict the mean and standard deviation of the critical gaps. Finally, the Maximum Likelihood method can predict reasonable estimates with observations for 25 to 30 drivers. A spreadsheet procedure for using the Maximum Likelihood method is provided in this paper. The PEM can be improved if the maximum rejected gap is used.

The effect of using different regions of interest on local and mean skin temperature

The dynamic nature of tissue temperature and the subcutaneous properties, such as blood flow, fatness, and metabolic rate, leads to variation in local skin temperature. Therefore, we investigated the effects of using multiple regions of interest when calculating weighted mean skin temperature from four local sites. Twenty-six healthy males completed a single trial in a thermonetural laboratory (mean ± SD): 24.0 (1.2) °C; 56 (8%) relative humidity; < 0.1 m/s air speed). Mean skin temperature was calculated from four local sites (neck, scapula, hand and shin) in accordance with International Standards using digital infrared thermography. A 50 x 50 mm square, defined by strips of aluminium tape, created six unique regions of interest, top left quadrant, top right quadrant, bottom left quadrant, bottom right quadrant, centre quadrant and the entire region of interest, at each of the local sites. The largest potential error in weighted mean skin temperature was calculated using a combination of a) the coolest and b) the warmest regions of interest at each of the local sites. Significant differences between the six regions interest were observed at the neck (P < 0.01), scapula (P < 0.001) and shin (P < 0.05); but not at the hand (P = 0.482). The largest difference (± SEM) at each site was as follows: neck 0.2 (0.1) °C; scapula 0.2 (0.0) °C; shin 0.1 (0.0) °C and hand 0.1 (0.1) °C. The largest potential error (mean ± SD) in weighted mean skin temperature was 0.4 (0.1) °C (P < 0.001) and the associated 95% limits of agreement for these differences was 0.2 to 0.5 °C. Although we observed differences in local and mean skin temperature based on the region of interest employed, these differences were minimal and are not considered physiologically meaningful.

A comparison between conductive and infrared devices for measuring mean skin temperature at rest, during exercise in the heat, and recovery

Purpose: Skin temperature assessment has historically been undertaken with conductive devices affixed to the skin. With the development of technology, infrared devices are increasingly utilised in the measurement of skin temperature. Therefore, our purpose was to evaluate the agreement between four skin temperature devices at rest, during exercise in the heat, and recovery. Methods: Mean skin temperature (T̅sk) was assessed in thirty healthy males during 30 min rest (24.0± 1.2°C, 56 ± 8%), 30 min cycle in the heat (38.0 ± 0.5°C, 41 ± 2%), and 45 min recovery(24.0 ± 1.3°C, 56 ± 9%). T̅sk was assessed at four sites using two conductive devices(thermistors, iButtons) and two infrared devices (infrared thermometer, infrared camera). Results: Bland–Altman plots demonstrated mean bias ± limits of agreement between the thermistors and iButtons as follows (rest, exercise, recovery): -0.01 ± 0.04, 0.26 ± 0.85, -0.37 ± 0.98°C; thermistors and infrared thermometer: 0.34 ± 0.44, -0.44 ± 1.23, -1.04 ± 1.75°C; thermistors and infrared camera (rest, recovery): 0.83 ± 0.77, 1.88 ± 1.87°C. Pairwise comparisons of T̅sk found significant differences (p < 0.05) between thermistors and both infrared devices during resting conditions, and significant differences between the thermistors and all other devices tested during exercise in the heat and recovery. Conclusions: These results indicate poor agreement between conductive and infrared devices at rest, during exercise in the heat, and subsequent recovery. Infrared devices may not be suitable for monitoring T̅sk in the presence of, or following, metabolic and environmental induced heat stress.

Scale adaptive tracking using mean shift and efficient feature matching

The mean shift tracker has achieved great success in visual object tracking due to its efficiency being nonparametric. However, it is still difficult for the tracker to handle scale changes of the object. In this paper, we associate a scale adaptive approach with the mean shift tracker. Firstly, the target in the current frame is located by the mean shift tracker. Then, a feature point matching procedure is employed to get the matched pairs of the feature point between target regions in the current frame and the previous frame. We employ FAST-9 corner detector and HOG descriptor for the feature matching. Finally, with the acquired matched pairs of the feature point, the affine transformation between target regions in the two frames is solved to obtain the current scale of the target. Experimental results show that the proposed tracker gives satisfying results when the scale of the target changes, with a good performance of efficiency.

What does the review of the Australian Curriculum mean for Senior Modern History?

In this paper we briefly explore some of recommendations of the Review of the Australian Curriculum Final Report (Australian Government, 2014a), henceforth referred to as the Review, with reference to Modern History in the senior secondary Australian Curriculum. We also refer to the invited papers provided by history subject matter specialists, Professor Gregory Melleuish and Mr Clive Logan, published as the Review’s Supplementary Material (Australian Government, 2014b). In doing so, we note that both documents devote most of their attention to critiquing the Australian Curriculum: History in the compulsory years from Foundation (F) to Year 10.

Introduction to Point and Counterpoint: What does the Review of the Australian Curriculum mean for History?

The April 2015 edition of Curriculum Perspectives has a special focus and casts light on the continuing development of the Australian Curriculum. This paper provides an introduction to a series of papers in the Point and Counterpoint section of this edition on the Review of the Australian Curriculum with reference to History. It makes clear that History is one of the most contested areas of the curriculum and that whilst politicians and policy makers are concerned with the importance of history in relation to national identity and nation building, history serves other purposes. The paper reiterates the need to pay attention to the particularities of discipline–based knowledge for the study of history in schools and the central role of inquiry for student learning in history. In doing so, it establishes the context for the five papers which follow.

What do Netflix, Stan and Presto mean for Australian TV?

The arrival of subscription video on demand services Netflix, Stan and Presto have implications for what we call "television" in Australia – and much of the policy detail remains to be hammered out.