Populations of models, experimental designs and coverage of parameter space by Latin Hypercube and Orthogonal Sampling

In this paper we have used simulations to make a conjecture about the coverage of a t-dimensional subspace of a d-dimensional parameter space of size n when performing k trials of Latin Hypercube sampling. This takes the form P(k,n,d,t) = 1 - e^(-k/n^(t-1)). We suggest that this coverage formula is independent of d and this allows us to make connections between building Populations of Models and Experimental Designs. We also show that Orthogonal sampling is superior to Latin Hypercube sampling in terms of allowing a more uniform coverage of the t-dimensional subspace at the sub-block size level. These ideas have particular relevance when attempting to perform uncertainty quantification and sensitivity analyses.

Stochastic linear multistep methods for the simulation of chemical kinetics

In this paper, we introduce the Stochastic Adams-Bashforth (SAB) and Stochastic Adams-Moulton (SAM) methods as an extension of the tau-leaping framework to past information. Using the theta-trapezoidal tau-leap method of weak order two as a starting procedure, we show that the k-step SAB method with k >= 3 is order three in the mean and correlation, while a predictor-corrector implementation of the SAM method is weak order three in the mean but only order one in the correlation. These convergence results have been derived analytically for linear problems and successfully tested numerically for both linear and non-linear systems. A series of additional examples have been implemented in order to demonstrate the efficacy of this approach.

Legal translation

Legal translation theory brooks little interference with the source legal text. With few exceptions (Joseph 2005; Hammel 2008; Harvey 2002; Kahaner 2005; Kasirer 2001; Lawson 2006), lawyers and linguists tend to tether themselves to the pole of literalism. More a tight elastic band than an unyielding rope, this tether constrains — rather than prohibits — liberal legal translations. It can stretch to accommodate a degree of freedom by the legal translator however, should it go too far, it snaps back to the default position of linguistic fidelity. This ‘stretch and snap’ gives legal translation a unique place in general translation theory. In the general debate over the ‘degree of freedom’ the translator enjoys in conveying the meaning of the text, legal translation theory has reached its own settlement. Passivity is the default; creativity, the ‘qualified’ exception (Hammel 2008: 275).

Fourier spectral methods for fractional-in-space reaction-diffusion equations

Fractional differential equations are becoming increasingly used as a powerful modelling approach for understanding the many aspects of nonlocality and spatial heterogeneity. However, the numerical approximation of these models is demanding and imposes a number of computational constraints. In this paper, we introduce Fourier spectral methods as an attractive and easy-to-code alternative for the integration of fractional-in-space reaction-diffusion equations described by the fractional Laplacian in bounded rectangular domains ofRn. The main advantages of the proposed schemes is that they yield a fully diagonal representation of the fractional operator, with increased accuracy and efficiency when compared to low-order counterparts, and a completely straightforward extension to two and three spatial dimensions. Our approach is illustrated by solving several problems of practical interest, including the fractional Allen–Cahn, FitzHugh–Nagumo and Gray–Scott models, together with an analysis of the properties of these systems in terms of the fractional power of the underlying Laplacian operator.

Fractional diffusion models of cardiac electrical propagation: Role of structural heterogeneity in dispersion of repolarization

Impulse propagation in biological tissues is known to be modulated by structural heterogeneity. In cardiac muscle, improved understanding on how this heterogeneity influences electrical spread is key to advancing our interpretation of dispersion of repolarization. We propose fractional diffusion models as a novel mathematical description of structurally heterogeneous excitable media, as a means of representing the modulation of the total electric field by the secondary electrical sources associated with tissue inhomogeneities. Our results, analysed against in vivo human recordings and experimental data of different animal species, indicate that structural heterogeneity underlies relevant characteristics of cardiac electrical propagation at tissue level. These include conduction effects on action potential (AP) morphology, the shortening of AP duration along the activation pathway and the progressive modulation by premature beats of spatial patterns of dispersion of repolarization. The proposed approach may also have important implications in other research fields involving excitable complex media.

Population of computational rabbit-specific ventricular action potential models for investigating sources of variability in cellular repolarisation

Variability is observed at all levels of cardiac electrophysiology. Yet, the underlying causes and importance of this variability are generally unknown, and difficult to investigate with current experimental techniques. The aim of the present study was to generate populations of computational ventricular action potential models that reproduce experimentally observed intercellular variability of repolarisation (represented by action potential duration) and to identify its potential causes. A systematic exploration of the effects of simultaneously varying the magnitude of six transmembrane current conductances (transient outward, rapid and slow delayed rectifier K(+), inward rectifying K(+), L-type Ca(2+), and Na(+)/K(+) pump currents) in two rabbit-specific ventricular action potential models (Shannon et al. and Mahajan et al.) at multiple cycle lengths (400, 600, 1,000 ms) was performed. This was accomplished with distributed computing software specialised for multi-dimensional parameter sweeps and grid execution. An initial population of 15,625 parameter sets was generated for both models at each cycle length. Action potential durations of these populations were compared to experimentally derived ranges for rabbit ventricular myocytes. 1,352 parameter sets for the Shannon model and 779 parameter sets for the Mahajan model yielded action potential duration within the experimental range, demonstrating that a wide array of ionic conductance values can be used to simulate a physiological rabbit ventricular action potential. Furthermore, by using clutter-based dimension reordering, a technique that allows visualisation of multi-dimensional spaces in two dimensions, the interaction of current conductances and their relative importance to the ventricular action potential at different cycle lengths were revealed. Overall, this work represents an important step towards a better understanding of the role that variability in current conductances may play in experimentally observed intercellular variability of rabbit ventricular action potential repolarisation.

The new Vancouver Chest Pain Rule using troponin as the only biomarker: An external validation study

Objectives To externally evaluate the accuracy of the new Vancouver Chest Pain Rule and to assess the diagnostic accuracy using either sensitive or highly sensitive troponin assays. Methods Prospectively collected data from 2 emergency departments (EDs) in Australia and New Zealand were analysed. Based on the new Vancouver Chest Pain Rule, low-risk patients were identified using electrocardiogram results, cardiac history, nitrate use, age, pain characteristics and troponin results at 2 hours after presentation. The primary outcome was 30-day diagnosis of acute coronary syndrome (ACS), including acute myocardial infarction, and unstable angina. Sensitivity, specificity, positive predictive values and negative predictive values were calculated to assess the accuracy of the new Vancouver Chest Pain Rule using either sensitive or highly sensitive troponin assay results. Results Of the 1635 patients, 20.4% had an ACS diagnosis at 30 days. Using the highly sensitive troponin assay, 212 (13.0%) patients were eligible for early discharge with 3 patients (1.4%) diagnosed with ACS. Sensitivity was 99.1% (95% CI 97.4-99.7), specificity was 16.1 (95% CI 14.2-18.2), positive predictive values was 23.3 (95% CI 21.1-25.5) and negative predictive values was 98.6 (95% CI 95.9-99.5). The diagnostic accuracy of the rule was similar using the sensitive troponin assay. Conclusions The new Vancouver Chest Pain Rule should be used for the identification of low risk patients presenting to EDs with symptoms of possible ACS, and will reduce the proportion of patients requiring lengthy assessment; however we recommend further outpatient investigation for coronary artery disease in patients identified as low risk.

Efficient simulation of stochastic chemical kinetics with the Stochastic Bulirsch-Stoer extrapolation method

Background Biochemical systems with relatively low numbers of components must be simulated stochastically in order to capture their inherent noise. Although there has recently been considerable work on discrete stochastic solvers, there is still a need for numerical methods that are both fast and accurate. The Bulirsch-Stoer method is an established method for solving ordinary differential equations that possesses both of these qualities. Results In this paper, we present the Stochastic Bulirsch-Stoer method, a new numerical method for simulating discrete chemical reaction systems, inspired by its deterministic counterpart. It is able to achieve an excellent efficiency due to the fact that it is based on an approach with high deterministic order, allowing for larger stepsizes and leading to fast simulations. We compare it to the Euler τ-leap, as well as two more recent τ-leap methods, on a number of example problems, and find that as well as being very accurate, our method is the most robust, in terms of efficiency, of all the methods considered in this paper. The problems it is most suited for are those with increased populations that would be too slow to simulate using Gillespie’s stochastic simulation algorithm. For such problems, it is likely to achieve higher weak order in the moments. Conclusions The Stochastic Bulirsch-Stoer method is a novel stochastic solver that can be used for fast and accurate simulations. Crucially, compared to other similar methods, it better retains its high accuracy when the timesteps are increased. Thus the Stochastic Bulirsch-Stoer method is both computationally efficient and robust. These are key properties for any stochastic numerical method, as they must typically run many thousands of simulations.

Stochastic dynamics of interacting haematopoietic stem cell niche lineages

Since we still know very little about stem cells in their natural environment, it is useful to explore their dynamics through modelling and simulation, as well as experimentally. Most models of stem cell systems are based on deterministic differential equations that ignore the natural heterogeneity of stem cell populations. This is not appropriate at the level of individual cells and niches, when randomness is more likely to affect dynamics. In this paper, we introduce a fast stochastic method for simulating a metapopulation of stem cell niche lineages, that is, many sub-populations that together form a heterogeneous metapopulation, over time. By selecting the common limiting timestep, our method ensures that the entire metapopulation is simulated synchronously. This is important, as it allows us to introduce interactions between separate niche lineages, which would otherwise be impossible. We expand our method to enable the coupling of many lineages into niche groups, where differentiated cells are pooled within each niche group. Using this method, we explore the dynamics of the haematopoietic system from a demand control system perspective. We find that coupling together niche lineages allows the organism to regulate blood cell numbers as closely as possible to the homeostatic optimum. Furthermore, coupled lineages respond better than uncoupled ones to random perturbations, here the loss of some myeloid cells. This could imply that it is advantageous for an organism to connect together its niche lineages into groups. Our results suggest that a potential fruitful empirical direction will be to understand how stem cell descendants communicate with the niche and how cancer may arise as a result of a failure of such communication.

Estimates on the coverage of parameter space using populations of models

In this paper we provide estimates for the coverage of parameter space when using Latin Hypercube Sampling, which forms the basis of building so-called populations of models. The estimates are obtained using combinatorial counting arguments to determine how many trials, k, are needed in order to obtain specified parameter space coverage for a given value of the discretisation size n. In the case of two dimensions, we show that if the ratio (Ø) of trials to discretisation size is greater than 1, then as n becomes moderately large the fractional coverage behaves as 1-exp-ø. We compare these estimates with simulation results obtained from an implementation of Latin Hypercube Sampling using MATLAB.

A stochastic exponential Euler scheme for simulation of stiff biochemical reaction systems

In order to simulate stiff biochemical reaction systems, an explicit exponential Euler scheme is derived for multidimensional, non-commutative stochastic differential equations with a semilinear drift term. The scheme is of strong order one half and A-stable in mean square. The combination with this and the projection method shows good performance in numerical experiments dealing with an alternative formulation of the chemical Langevin equation for a human ether a-go-go related gene ion channel mode

Post-transcriptional regulation in the nucleus and cytoplasm: study of mean time to threshold (MTT) and narrow escape problem

Messenger RNAs (mRNAs) can be repressed and degraded by small non-coding RNA molecules. In this paper, we formulate a coarsegrained Markov-chain description of the post-transcriptional regulation of mRNAs by either small interfering RNAs (siRNAs) or microRNAs (miRNAs). We calculate the probability of an mRNA escaping from its domain before it is repressed by siRNAs/miRNAs via cal- culation of the mean time to threshold: when the number of bound siRNAs/miRNAs exceeds a certain threshold value, the mRNA is irreversibly repressed. In some cases,the analysis can be reduced to counting certain paths in a reduced Markov model. We obtain explicit expressions when the small RNA bind irreversibly to the mRNA and we also discuss the reversible binding case. We apply our models to the study of RNA interference in the nucleus, examining the probability of mRNAs escaping via small nuclear pores before being degraded by siRNAs. Using the same modelling framework, we further investigate the effect of small, decoy RNAs (decoys) on the process of post-transcriptional regulation, by studying regulation of the tumor suppressor gene, PTEN : decoys are able to block binding sites on PTEN mRNAs, thereby educing the number of sites available to siRNAs/miRNAs and helping to protect it from repression. We calculate the probability of a cytoplasmic PTEN mRNA translocating to the endoplasmic reticulum before being repressed by miRNAs. We support our results with stochastic simulations

Nutritional status and the foraging behaviour of Bactrocera tryoni with particular reference to protein bait spray

Poisoned protein baits comprise a recognized method for controlling tephritid fruit flies in the form of a ‘lure-and-kill’ technique. However, little is known about how a fly's internal protein and carbohydrate levels (i.e. nutritional status) might influence the efficacy of this control. In the present study, the relationships between the internal levels of protein (as measured by total body nitrogen) and carbohydrate (as measured by total body carbon) of the fruit fly Bactrocera tryoni (Froggatt) (Diptera: Tephritidae) are investigated, as well as its foraging behaviours in response to protein, fruit and cue-lure (a male-specific attractant) baits. Small cage behavioural experiments are conducted using flies from cultures of different nutritional status and wild flies sampled from the field during the fruiting cycle of a guava crop. For female flies, increasing total body nitrogen is correlated with decreased protein foraging and increased oviposition activity; increasing total body carbon levels generate the same behavioural changes except that the oviposition response is not significant. For males, there are no significant correlations between changes in total body nitrogen and total body carbon and protein or cue-lure foraging. For wild flies from the guava orchard, almost all of them are sexually mature when entering the crop and, over the entire season, total body nitrogen and total body carbon levels are such that protein hunger is unlikely for most flies. The results infer strongly that the requirements of wild, sexually mature flies for protein are minimal and that flies can readily gain sufficient nutrients from wild sources for their physiological needs. The results offer a mechanistic explanation for the poor response of male and mature female fruit flies to protein bait spray.

Triaging older major trauma patients in the emergency department: An observational study

Background The objective of this study was to compare the triage category assigned to older trauma patients with younger trauma patients upon arrival to the emergency department. The focus was to examine whether older major trauma patients were less likely to be assigned an emergency triage category on arrival to the emergency department after controlling for relevant demographics, injury characteristics and injury severity. Methods This was an observational study using data from the Queensland Trauma Registry. All trauma patients aged 15 years and older who presented to contributing hospitals between 1 January 2005 and 31 December 2009 with an Injury Severity Score (ISS)>15 were included. Logistic regression analysis examined the odds of assignment to emergency (Australasian Triage Scale (ATS) 1 or 2) versus urgent (ATS 3–5) treatment for patients across various age categories after adjustment for relevant demographics, injury characteristics and injury severity. Results The study used data on 6923 patients with a median (IQR) age of 43 (26–62) years and a mortality of 11.4% (95% CI 10.7% to 12.2%). Compared with individuals aged 15–34, the adjusted odds of being assigned an ATS category 1 or 2 were 30% lower (OR=0.68, 95% CI 0.57 to 0.81) for individuals aged 55–75 years and were 50% lower (OR=0.46, 95% CI 0.37 to 0.56) for individuals aged 75 years or older. Conclusions Among patients with an ISS>15, older major trauma patients were less likely to be assigned an emergency triage category compared with younger patients. This suggests that the elderly may be undertriaged and provides a potential area of study for reducing mortality and morbidity in older

Statistical literacy social media project for the masses

This article examines a social media assignment used to teach and practice statistical literacy with over 400 students each semester in large-lecture traditional, fully online, and flipped sections of an introductory-level statistics course. Following the social media assignment, students completed a survey on how they approached the assignment. Drawing from the authors’ experiences with the project and the survey results, this article offers recommendations for developing social media assignments in large courses that focus on the interplay between the social media tool and the implications of assignment prompts.