A sequential Monte Carlo algorithm to incorporate model uncertainty in Bayesian sequential design

Here we present a sequential Monte Carlo (SMC) algorithm that can be used for any one-at-a-time Bayesian sequential design problem in the presence of model uncertainty where discrete data are encountered. Our focus is on adaptive design for model discrimination but the methodology is applicable if one has a different design objective such as parameter estimation or prediction. An SMC algorithm is run in parallel for each model and the algorithm relies on a convenient estimator of the evidence of each model which is essentially a function of importance sampling weights. Other methods for this task such as quadrature, often used in design, suffer from the curse of dimensionality. Approximating posterior model probabilities in this way allows us to use model discrimination utility functions derived from information theory that were previously difficult to compute except for conjugate models. A major benefit of the algorithm is that it requires very little problem specific tuning. We demonstrate the methodology on three applications, including discriminating between models for decline in motor neuron numbers in patients suffering from neurological diseases such as Motor Neuron disease.

A continuum model of the growth of engineered epidermal skin substitutes

We present a porous medium model of the growth and deterioration of the viable sublayers of an epidermal skin substitute. It consists of five species: cells, intracellular and extracellular calcium, tight junctions, and a hypothesised signal chemical emanating from the stratum corneum. The model is solved numerically in Matlab using a finite difference scheme. Steady state calcium distributions are predicted that agree well with the experimental data. Our model also demonstrates epidermal skin substitute deterioration if the calcium diffusion coefficient is reduced compared to reported values in the literature.

A boundary preserving numerical algorithm for the Wright-Fisher model with mutation

The Wright-Fisher model is an Itô stochastic differential equation that was originally introduced to model genetic drift within finite populations and has recently been used as an approximation to ion channel dynamics within cardiac and neuronal cells. While analytic solutions to this equation remain within the interval [0,1], current numerical methods are unable to preserve such boundaries in the approximation. We present a new numerical method that guarantees approximations to a form of Wright-Fisher model, which includes mutation, remain within [0,1] for all time with probability one. Strong convergence of the method is proved and numerical experiments suggest that this new scheme converges with strong order 1/2. Extending this method to a multidimensional case, numerical tests suggest that the algorithm still converges strongly with order 1/2. Finally, numerical solutions obtained using this new method are compared to those obtained using the Euler-Maruyama method where the Wiener increment is resampled to ensure solutions remain within [0,1].

Simulating a latent susceptible pool to examine the impact on cardiovascular mortality

The health effects of cold and hot temperatures are strongest in the frail and elderly. A large number of deaths in this "susceptible pool" after heat waves and cold snaps can cause mortality displacement, where an immediate increase in mortality is somewhat offset by a subsequent decrease in the following weeks. There may also be longer-term implications, as reductions in the pool caused by hot summers can reduce cold-related mortality in the following winter. A state-space model was used to simulate the numbers in the susceptible pool over time. We simulated the effects of harsh winters and heat waves, and varied the size of the susceptible pool. The larger the susceptible pool the smaller the mortality displacement. When 1% of the population were susceptible a harsh winter lead to an average of just 3 months of life lost per cold-related death, whereas a pool size of 10% meant that 24 months of life were lost per death. The impact of a cold spell on months of life lost was greater when the increased risk of death also applied to healthy people. The number of deaths caused by an August heat wave were reduced when there was a prior heat wave in June which reduced the susceptible pool. We were able to mimic some observed seasonal patterns in mortality using a simple state-space model. A better understanding of the size and dynamics of the susceptible pool will improve our understanding of the health effects of temperature.

An implicit RBF meshless method for a fractal mobile/immobile transport model

Fractional differential equation is used to describe a fractal model of mobile/immobile transport with a power law memory function. This equation is the limiting equation that governs continuous time random walks with heavy tailed random waiting times. In this paper, we firstly propose a finite difference method to discretize the time variable and obtain a semi-discrete scheme. Then we discuss its stability and convergence. Secondly we consider a meshless method based on radial basis functions (RBF) to discretize the space variable. By contrast to conventional FDM and FEM, the meshless method is demonstrated to have distinct advantages: calculations can be performed independent of a mesh, it is more accurate and it can be used to solve complex problems. Finally the convergence order is verified from a numerical example is presented to describe the fractal model of mobile/immobile transport process with different problem domains. The numerical results indicate that the present meshless approach is very effective for modeling and simulating of fractional differential equations, and it has good potential in development of a robust simulation tool for problems in engineering and science that are governed by various types of fractional differential equations.

Numerical analysis of the time variable fractional order mobile-immobile advection-dispersion model

Many physical processes exhibit fractional order behavior that varies with time or space. The continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable. In this paper, we consider the time variable fractional order mobile-immobile advection-dispersion model. Numerical methods and analyses of stability and convergence for the fractional partial differential equations are quite limited and difficult to derive. This motivates us to develop efficient numerical methods as well as stability and convergence of the implicit numerical methods for the fractional order mobile immobile advection-dispersion model. In the paper, we use the Coimbra variable time fractional derivative which is more efficient from the numerical standpoint and is preferable for modeling dynamical systems. An implicit Euler approximation for the equation is proposed and then the stability of the approximation are investigated. As for the convergence of the numerical scheme we only consider a special case, i.e. the time fractional derivative is independent of time variable t. The case where the time fractional derivative depends both the time variable t and the space variable x will be considered in the future work. Finally, numerical examples are provided to show that the implicit Euler approximation is computationally efficient.

An improved model of tumour-immune system interactions

The immune system plays an important role in defending the body against tumours and other threats. Currently, mechanisms involved in immune system interactions with tumour cells are not fully understood. Here we develop a mathematical tool that can be used in aiding to address this shortfall in understanding. This paper de- scribes a hybrid cellular automata model of the interaction between a growing tumour and cells of the innate and specific immune system including the effects of chemokines that builds on previous models of tumour-immune system interactions. In particular, the model is focused on the response of immune cells to tumour cells and how the dynamics of the tumour cells change due to the immune system of the host. We present results and predictions of in silico experiments including simulations of Kaplan-Meier survival-like curves.

A safety adapted car following model for traffic safety studies

Traffic safety studies demand more than what current micro-simulation models can provide as they presume that all drivers exhibit safe behaviors. All the microscopic traffic simulation models include a car following model. This paper highlights the limitations of the Gipps car following model ability to emulate driver behavior for safety study purposes. A safety adapted car following model based on the Gipps car following model is proposed to simulate unsafe vehicle movements, with safety indicators below critical thresholds. The modifications are based on the observations of driver behavior in real data and also psychophysical notions. NGSIM vehicle trajectory data is used to evaluate the new model and short following headways and Time To Collision are employed to assess critical safety events within traffic flow. Risky events are extracted from available NGSIM data to evaluate the modified model against them. The results from simulation tests illustrate that the proposed model can predict the safety metrics better than the generic Gipps model. The outcome of this paper can potentially facilitate assessing and predicting traffic safety using microscopic simulation.

Is the unigram relevance model term independent? Classifying term dependencies in query expansion

This paper develops a framework for classifying term dependencies in query expansion with respect to the role terms play in structural linguistic associations. The framework is used to classify and compare the query expansion terms produced by the unigram and positional relevance models. As the unigram relevance model does not explicitly model term dependencies in its estimation process it is often thought to ignore dependencies that exist between words in natural language. The framework presented in this paper is underpinned by two types of linguistic association, namely syntagmatic and paradigmatic associations. It was found that syntagmatic associations were a more prevalent form of linguistic association used in query expansion. Paradoxically, it was the unigram model that exhibited this association more than the positional relevance model. This surprising finding has two potential implications for information retrieval models: (1) if linguistic associations underpin query expansion, then a probabilistic term dependence assumption based on position is inadequate for capturing them; (2) the unigram relevance model captures more term dependency information than its underlying theoretical model suggests, so its normative position as a baseline that ignores term dependencies should perhaps be reviewed.

A tensor encoding model for semantic processing

This paper develops and evaluates an enhanced corpus based approach for semantic processing. Corpus based models that build representations of words directly from text do not require pre-existing linguistic knowledge, and have demonstrated psychologically relevant performance on a number of cognitive tasks. However, they have been criticised in the past for not incorporating sufficient structural information. Using ideas underpinning recent attempts to overcome this weakness, we develop an enhanced tensor encoding model to build representations of word meaning for semantic processing. Our enhanced model demonstrates superior performance when compared to a robust baseline model on a number of semantic processing tasks.

Seasonal variation in cardiovascular disease risk factors in a subarctic population : the Tromso Study 1979-2008

Background Seasonal changes in cardiovascular disease (CVD) risk factors may be due to exposure to seasonal environmental variables like temperature and acute infections or seasonal behavioural patterns in physical activity and diet. Investigating the seasonal pattern of risk factors should help determine the causes of the seasonal pattern in CVD. Few studies have investigated the seasonal variation in risk factors using repeated measurements from the same individual, which is important as individual and population seasonal patterns may differ. Methods The authors investigated the seasonal pattern in systolic and diastolic blood pressure, heart rate, body weight, total cholesterol, triglycerides, high-density lipoprotein cholesterol, C reactive protein and fibrinogen. Measurements came from 38 037 participants in the population-based cohort, the Tromsø Study, examined up to eight times from 1979 to 2008. Individual and population seasonal patterns were estimated using a cosinor in a mixed model. Results All risk factors had a highly statistically significant seasonal pattern with a peak time in winter, except for triglycerides (peak in autumn), C reactive protein and fibrinogen (peak in spring). The sizes of the seasonal variations were clinically modest. Conclusions Although the authors found highly statistically significant individual seasonal patterns for all risk factors, the sizes of the changes were modest, probably because this subarctic population is well adapted to a harsh climate. Better protection against seasonal risk factors like cold weather could help reduce the winter excess in CVD observed in milder climates.

Reversal of acute coagulopathy during hypotensive resuscitation using small-volume 7.5% NaCl adenocaine and Mg2+ in the rat model of severe hemorrhagic shock

OBJECTIVE: : Acute traumatic coagulopathy occurs early in hemorrhagic trauma and is a major contributor to mortality and morbidity. Our aim was to examine the effect of small-volume 7.5% NaCl adenocaine (adenosine and lidocaine, adenocaine) and Mg on hypotensive resuscitation and coagulopathy in the rat model of severe hemorrhagic shock. DESIGN: : Prospective randomized laboratory investigation. SUBJECTS: : A total of 68 male Sprague Dawley Rats. INTERVENTION: : Post-hemorrhagic shock treatment for acute traumatic coagulopathy. MEASUREMENTS AND METHODS: : Nonheparinized male Sprague-Dawley rats (300-450 g, n = 68) were randomly assigned to either: 1) untreated; 2) 7.5% NaCl; 3) 7.5% NaCl adenocaine; 4) 7.5% NaCl Mg; or 5) 7.5% NaCl adenocaine/Mg. Hemorrhagic shock was induced by phlebotomy to mean arterial pressure of 35-40 mm Hg for 20 mins (~40% blood loss), and animals were left in shock for 60 mins. Bolus (0.3 mL) was injected into the femoral vein and hemodynamics monitored. Blood was collected in Na citrate (3.2%) tubes, centrifuged, and the plasma snap frozen in liquid N2 and stored at -80°C. Coagulation was assessed using activated partial thromboplastin times and prothrombin times. RESULTS: : Small-volume 7.5% NaCl adenocaine and 7.5% NaCl adenocaine/Mg were the only two groups that gradually increased mean arterial pressure 1.6-fold from 38-39 mm Hg to 52 and 64 mm Hg, respectively, at 60 mins (p < .05). Baseline plasma activated partial thromboplastin time was 17 ± 0.5 secs and increased to 63 ± 21 secs after bleeding time, and 217 ± 32 secs after 60-min shock. At 60-min resuscitation, activated partial thromboplastin time values for untreated, 7.5% NaCl, 7.5% NaCl/Mg, and 7.5% NaCl adenocaine rats were 269 ± 31 secs, 262 ± 38 secs, 150 ± 43 secs, and 244 ± 38 secs, respectively. In contrast, activated partial thromboplastin time for 7.5% NaCl adenocaine/Mg was 24 ± 2 secs (p < .05). Baseline prothrombin time was 28 ± 0.8 secs (n = 8) and followed a similar pattern of correction. CONCLUSIONS: : Plasma activated partial thromboplastin time and prothrombin time increased over 10-fold during the bleed and shock periods prior to resuscitation, and a small-volume (~1 mL/kg) IV bolus of 7.5% NaCl AL/Mg was the only treatment group that raised mean arterial pressure into the permissive range and returned activated partial thromboplastin time and prothrombin time clotting times to baseline at 60 mins.

A hybrid model for studying spatial aspects of infectious diseases

We consider a hybrid model, created by coupling a continuum and an agent-based model of infectious disease. The framework of the hybrid model provides a mechanism to study the spread of infection at both the individual and population levels. This approach captures the stochastic spatial heterogeneity at the individual level, which is directly related to deterministic population level properties. This facilitates the study of spatial aspects of the epidemic process. A spatial analysis, involving counting the number of infectious agents in equally sized bins, reveals when the spatial domain is nonhomogeneous.