Mean-field descriptions of collective migration with strong adhesion

Random walk models based on an exclusion process with contact effects are often used to represent collective migration where individual agents are affected by agent-to-agent adhesion. Traditional mean field representations of these processes take the form of a nonlinear diffusion equation which, for strong adhesion, does not predict the averaged discrete behavior. We propose an alternative suite of mean-field representations, showing that collective migration with strong adhesion can be accurately represented using a moment closure approach.

Estimating the effects of environmental exposures using a weighted mean of monitoring stations

The health effects of environmental hazards are often examined using time series of the association between a daily response variable (e.g., death) and a daily level of exposure (e.g., temperature). Exposures are usually the average from a network of stations. This gives each station equal importance, and negates the opportunity for some stations to be better measures of exposure. We used a Bayesian hierarchical model that weighted stations using random variables between zero and one. We compared the weighted estimates to the standard model using data on health outcomes (deaths and hospital admissions) and exposures (air pollution and temperature) in Brisbane, Australia. The improvements in model fit were relatively small, and the estimated health effects of pollution were similar using either the standard or weighted estimates. Spatial weighted exposures would be probably more worthwhile when there is either greater spatial detail in the health outcome, or a greater spatial variation in exposure.

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.

Optimal Bayesian experimental design for models with intractable likelihoods using indirect inference applied to biological process models

This paper addresses the problem of determining optimal designs for biological process models with intractable likelihoods, with the goal of parameter inference. The Bayesian approach is to choose a design that maximises the mean of a utility, and the utility is a function of the posterior distribution. Therefore, its estimation requires likelihood evaluations. However, many problems in experimental design involve models with intractable likelihoods, that is, likelihoods that are neither analytic nor can be computed in a reasonable amount of time. We propose a novel solution using indirect inference (II), a well established method in the literature, and the Markov chain Monte Carlo (MCMC) algorithm of Müller et al. (2004). Indirect inference employs an auxiliary model with a tractable likelihood in conjunction with the generative model, the assumed true model of interest, which has an intractable likelihood. Our approach is to estimate a map between the parameters of the generative and auxiliary models, using simulations from the generative model. An II posterior distribution is formed to expedite utility estimation. We also present a modification to the utility that allows the Müller algorithm to sample from a substantially sharpened utility surface, with little computational effort. Unlike competing methods, the II approach can handle complex design problems for models with intractable likelihoods on a continuous design space, with possible extension to many observations. The methodology is demonstrated using two stochastic models; a simple tractable death process used to validate the approach, and a motivating stochastic model for the population evolution of macroparasites.

Low-phosporous nickel-coated carbon microcoils : Controlling microstructure through an electroless plating process

Carbon microcoils (CMCs) have been coated with a nickel-phosphorus (Ni-P) film using an electroless plating process, with sodium hypophosphite as a reducing agent in an alkaline bath. CMC composites have potential applications as microwave absorption materials. The morphology, elemental composition and phases in the coating layer of the CMCs and Ni-coated CMCs were investigated by scanning electron microscopy (SEM), energy dispersive spectroscopy (EDS) and X-ray diffraction (XRD), respectively. The effects of process parameters such as pH, temperature and coating time of the plating bath on the phosphorus content and deposition rate of the electroless Ni-P coating were studied. The results revealed that a continuous, uniform and low-phosphorous nickel coating was deposited on the surface of the CMCs for 20 min at pH 9.0, plating bath temperature 70 °C. The as-deposited coatings with approximately 4.5 wt.% phosphorus were found to consist of a mix of nano- and microcrystalline phases. The mean particle size of Ni-P nanoparticles on the outer surface of the CMCs was around 11.9 nm. The deposition rate was found to moderately increase with increasing pH, whereas, the phosphorous content of the deposit exhibited a significant decrease. Moreover, the material of the coating underwent a phase transition between an amorphous and a crystalline structure. The thickness of the deposit and the deposition rate may be controlled through careful variation of the coating time and plating bath temperature.

Process considerations related to the microencapsulation of plasmid DNA via ultrasonic atomization

An effective means of facilitating DNA vaccine delivery to antigen presenting cells is through biodegradable microspheres. Microspheres offer distinct advantages over other delivery technologies by providing release of DNA vaccine in its bioactive form in a controlled fashion. In this study, biodegradable poly(D,L-lactide-coglycolide) (PLGA) microspheres containing polyethylenimine (PEI) condensed plasmid DNA (pDNA) were prepared using a 40 kHz ultrasonic atomization system. Process synthesis parameters, which are important to the scale-up of microspheres that are suitable for nasal delivery (i.e., less than 20 μm), were studied. These parameters include polymer concentration; feed flowrate; volumetric ratio of polymer and pDNA-PEI (plasmid DNA-polyethylenimine) complexes; and nitrogen to phosphorous (N/P) ratio. PDNA encapsulation efficiencies were predominantly in the range 82-96%, and the mean sizes of the particle were between 6 and 15 μm. The ultrasonic synthesis method was shown to have excellent reproducibility. PEI affected morphology of the microspheres, as it induced the formation of porous particles that accelerate the release rate of pDNA. The PLGA microspheres displayed an in vitro release of pDNA of 95-99% within 30 days and demonstrated zero order release kinetics without an initial spike of pDNA. Agarose electrophoresis confirmed conservation of the supercoiled form of pDNA throughout the synthesis and in vitro release stages. It was concluded that ultrasonic atomization is an efficient technique to overcome the key obstacles in scaling-up the manufacture of encapsulated vaccine for clinical trials and ultimately, commercial applications.

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.

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

Precipitation In Small Systems--II. Mean Field Equations More Effective Than Population Balance

Part I (Manjunath et al., 1994, Chem. Engng Sci. 49, 1451-1463) of this paper showed that the random particle numbers and size distributions in precipitation processes in very small drops obtained by stochastic simulation techniques deviate substantially from the predictions of conventional population balance. The foregoing problem is considered in this paper in terms of a mean field approximation obtained by applying a first-order closure to an unclosed set of mean field equations presented in Part I. The mean field approximation consists of two mutually coupled partial differential equations featuring (i) the probability distribution for residual supersaturation and (ii) the mean number density of particles for each size and supersaturation from which all average properties and fluctuations can be calculated. The mean field equations have been solved by finite difference methods for (i) crystallization and (ii) precipitation of a metal hydroxide both occurring in a single drop of specified initial supersaturation. The results for the average number of particles, average residual supersaturation, the average size distribution, and fluctuations about the average values have been compared with those obtained by stochastic simulation techniques and by population balance. This comparison shows that the mean field predictions are substantially superior to those of population balance as judged by the close proximity of results from the former to those from stochastic simulations. The agreement is excellent for broad initial supersaturations at short times but deteriorates progressively at larger times. For steep initial supersaturation distributions, predictions of the mean field theory are not satisfactory thus calling for higher-order approximations. The merit of the mean field approximation over stochastic simulation lies in its potential to reduce expensive computation times involved in simulation. More effective computational techniques could not only enhance this advantage of the mean field approximation but also make it possible to use higher-order approximations eliminating the constraints under which the stochastic dynamics of the process can be predicted accurately.

The impact of a streamlined funding application process on application time: Two cross-sectional surveys of Australian researchers

Objective: To examine if streamlining a medical research funding application process saved time for applicants. Design: Cross-sectional surveys before and after the streamlining. Setting: The National Health and Medical Research Council (NHMRC) of Australia. Participants: Researchers who submitted one or more NHMRC Project Grant applications in 2012 or 2014. Main outcome measures: Average researcher time spent preparing an application and the total time for all applications in working days. Results: The average time per application increased from 34 working days before streamlining (95% CI 33 to 35) to 38 working days after streamlining (95% CI 37 to 39; mean difference 4 days, bootstrap p value <0.001). The estimated total time spent by all researchers on applications after streamlining was 614 working years, a 67-year increase from before streamlining. Conclusions: Streamlined applications were shorter but took longer to prepare on average. Researchers may be allocating a fixed amount of time to preparing funding applications based on their expected return, or may be increasing their time in response to increased competition. Many potentially productive years of researcher time are still being lost to preparing failed applications.

Plasma diagnostics of the high pressure oxygen-sputtering process

The characteristics of the high pressure oxygen-sputtering plasma in the pressure range 0.8–2.4 mbar have been studied using the Langmuir probe technique. The variation in plasma parameters such as positive ion density, electron density, mean electron energy and floating potential with pressure and temperature has been investigated. It has been observed that the positive ion density increases at high substrate temperatures whereas the negative ion density decreases. The study of the variation in mean electron energy and floating potential also indicated the possibility that the number of negative ions is less when the substrates are at elevated temperatures. Since the negative ions are supposed to cause re-sputtering and make the films off-stoichiometric, the reduction in the negative ion density as observed at elevated substrate temperatures is better suited for depositing stoichiometric YBa2Cu3O7−δ superconducting thin films.

Asymptotics of the invariant measure in mean field models with jumps

We consider the asymptotics of the invariant measure for the process of spatial distribution of N coupled Markov chains in the limit of a large number of chains. Each chain reflects the stochastic evolution of one particle. The chains are coupled through the dependence of transition rates on the spatial distribution of particles in the various states. Our model is a caricature for medium access interactions in wireless local area networks. Our model is also applicable in the study of spread of epidemics in a network. The limiting process satisfies a deterministic ordinary differential equation called the McKean-Vlasov equation. When this differential equation has a unique globally asymptotically stable equilibrium, the spatial distribution converges weakly to this equilibrium. Using a control-theoretic approach, we examine the question of a large deviation from this equilibrium.

Process control of cantilever deflection for sensor application based on optical waveguides

This paper reports on the fabrication of cantilever silicon-on-insulator (SOI) optical waveguides and presents solutions to the challenges of using a very thin 260-nm active silicon layer in the SOI structure to enable single-transverse-mode operation of the waveguide with minimal optical transmission losses. In particular, to ameliorate the anchor effect caused by the mean stress difference between the active silicon layer and buried oxide layer, a cantilever flattening process based on Ar plasma treatment is developed and presented. Vertical deflections of 0.5 mu m for 70-mu m-long cantilevers are mitigated to within few nanometers. Experimental investigations of cantilever mechanical resonance characteristics confirm the absence of significant detrimental side effects. Optical and mechanical modeling is extensively used to supplement experimental observations. This approach can satisfy the requirements for on-chip simultaneous readout of many integrated cantilever sensors in which the displacement or resonant frequency changes induced by analyte absorption are measured using an optical-waveguide-based division multiplexed system.

Fault Tolerance on Large Scale Systems using Adaptive Process Replication

Exascale systems of the future are predicted to have mean time between failures (MTBF) of less than one hour. At such low MTBFs, employing periodic checkpointing alone will result in low efficiency because of the high number of application failures resulting in large amount of lost work due to rollbacks. In such scenarios, it is highly necessary to have proactive fault tolerance mechanisms that can help avoid significant number of failures. In this work, we have developed a mechanism for proactive fault tolerance using partial replication of a set of application processes. Our fault tolerance framework adaptively changes the set of replicated processes periodically based on failure predictions to avoid failures. We have developed an MPI prototype implementation, PAREP-MPI that allows changing the replica set. We have shown that our strategy involving adaptive process replication significantly outperforms existing mechanisms providing up to 20 percent improvement in application efficiency even for exascale systems.