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.

Women and ADR

Alternative dispute resolution, or ‘ADR’, is defined by the National Alternative Dispute Resolution Advisory Council as: … an umbrella term for processes, other than judicial determination, in which an impartial person assists those in a dispute to resolve the issues between them. ADR is commonly used as an abbreviation for alternative dispute resolution, but can also be used to mean assisted or appropriate dispute resolution. Some also use the term ADR to include approaches that enable parties to prevent or manage their own disputes without outside assistance. A broad range of ADR processes are used in legal practice contexts, including, for example, arbitration, conciliation, mediation, negotiation, conferencing, case appraisal and neutral evaluation. Hybrid processes are also used, such as med-arb in which the practitioner starts by using mediation, and then shifts to using arbitration. ADR processes generally fall into one of three general categories: facilitative, advisory or determinative. In a facilitative process, the ADR practitioner has the role of assisting the parties to reach a mutually agreeable outcome to the dispute by helping them to identify the issues in dispute, and to develop a range of options for resolving the dispute. Mediation and facilitated negotiation are examples of facilitative processes. ADR processes that are advisory involve the practitioner appraising the dispute, providing advice as to the facts of the dispute, the law and then, in some cases, articulating possible or appropriate outcomes and how they might be achieved. Case appraisal and neutral evaluation are examples of advisory processes. In a determinative ADR process, the practitioner evaluates the dispute (which may include the hearing of formal evidence from the parties) and makes a determination. Arbitration is an example of a determinative ADR process. The use of ADR processes has increased significantly in recent years. Indeed, in a range of contemporary legal contexts the use of an ADR process is now required before a party is able to file a matter in court. For example, Juliet Behrens discusses in Chapter 11 of this book how the Family Law Act 1975 (Cth) now effectively mandates attendance at pre-filing family dispute resolution in parenting disputes. At the state level, in Queensland, for example, attendance at a conciliation conference can be required in anti-discrimination matters, and is encouraged in residential tenancy matters, and in personal injuries matters the parties must attend a preliminary compulsory conference. Certain ADR processes are used more commonly in the resolution of particular disputes. For example, in family law contexts, mediation and conciliation are generally used because they provide the parties with flexibility in terms of process and outcome while still ensuring that the negotiations occur in a positive, structured and facilitated framework. In commercial contexts, arbitration and neutral evaluation are often used because they can provide the parties with a determination of the dispute that is factually and legally principled, but which is also private and more timely than if the parties went to court. Women, as legal personalities and citizens of society, can find themselves involved in any sort of legal dispute, and therefore all forms of ADR are relevant to women. Perhaps most commonly, however, women come into contact with facilitative ADR processes. For example, through involvement in family law disputes women will encounter family dispute resolution processes, such as mediation. In this chapter, therefore, the focus is on facilitative ADR processes and, particularly, issues for women in terms of their participation in such processes. The aim of this chapter is to provide legal practitioners with an understanding of issues for women in ADR to inform your approach to representing women clients in such processes, and to guide you in preparing women clients for their participation in ADR. The chapter begins with a consideration of the ways in which facilitative ADR processes are positive for women participants. Next, some of the disadvantages for women in ADR are explored. Finally, the chapter offers ways in which legal practitioners can effectively prepare women clients for participation in ADR. Before embarking on a discussion of issues for women in ADR, it is important to acknowledge that women’s experiences in these dispute resolution environments, whilst often sharing commonalities, are diverse and informed by a range of factors specific to each individual woman; for example, her race or socio-economic background. This discussion, therefore, addresses some common issues for women in ADR that are fundamentally gender based. It must be noted, however, that providing advice to women clients about participating in ADR processes requires legal practitioners to have a very good understanding of the client as an individual, and her particular needs and interests. Some sources of diversity are discussed in Chapters 13, 14 and 15.

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

Crossover from Ising to mean-field critical behavior in an aqueous electrolyte solution

The near-critical behavior of the susceptibility deduced from light-scattering measurements in a ternary liquid mixture of 3-methylpyridine, water, and sodium bromide has been determined. The measurements have been performed in the one-phase region near the lower consolute points of samples with different concentrations of sodium bromide. A crossover from Ising asymptotic behavior to mean-field behavior has been observed. As the concentration of sodium bromide increases, the crossover becomes more pronounced, and the crossover temperature shifts closer to the critical temperature. The data are well described by a model that contains two independent crossover parameters. The crossover of the susceptibility critical exponent γ from its Ising value γ=1.24 to the mean-field value γ=1 is sharp and nonmonotonic. We conclude that there exists an additional length scale in the system due to the presence of the electrolyte which competes with the correlation length of the concentration fluctuations. An analogy with crossover phenomena in polymer solutions and a possible connection with multicritical phenomena is discussed.

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 Duet between the Author and the Translator: An Analysis of Style through Shifts in Literary Translation

The study proposes a method for identifying the personal imprint of literary translators in translated works of fiction. The initial assumption was that the style of a target text is not determined solely by the literary style of the author but also by features of its translator s idiolect. A method was developed for identifying the idiolectal features of individual translators, which were then used to describe personal translation styles. The method is not restricted to a particular language pair. To test the method and to establish the nature of the proposed personal imprint empirically, extracts from four English-language literary source texts (two novels by James Joyce and two by Ernest Hemingway) were first compared with their translations into Finnish (by four different translators) in order to identify changes, or shifts, that had taken place at the formal linguistic level in the translation process. To allow individual propensities to manifest themselves, only optional shifts in which the translators had a range of choices available to them were included in the study. In the second phase, extracts by different authors rendered into Finnish by the same translator were compared in order to gauge the extent of the potential impact of the author's style on the translator's work. In-depth analysis of the types of shifts made most frequently by the individual translators revealed further intersubjective differences, and the shifts were used to construct translation profiles for each of the translators. In order to determine the potential effects of frequently occurring shifts on the target text, some central concepts of narratology were adapted and used to establish an intermediate link between microlevel choices and macrolevel effects. In this way the propensity of an individual translator to opt for certain types of shift could be linked with the overall artistic effect of the target text.

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.

Tendency toward crossover of the effective susceptibility exponent from its doubled Ising value to its doubled mean-field value near a double critical point

The critical behavior of osmotic susceptibility in an aqueous electrolyte mixture 1-propanol (1P)+water (W)+potassium chloride is reported. This mixture exhibits re-entrant phase transitions and has a nearly parabolic critical line with its apex representing a double critical point (DCP). The behavior of the susceptibility exponent is deduced from static light-scattering measurements, on approaching the lower critical solution temperatures (TL’s) along different experimental paths (by varying t) in the one-phase region. The light-scattering data analysis substantiates the existence of a nonmonotonic crossover behavior of the susceptibility exponent in this mixture. For the TL far away from the DCP, the effective susceptibility exponent γeff as a function of t displays a nonmonotonic crossover from its single limit three-dimensional (3D)-Ising value ( ∼ 1.24) toward its mean-field value with increase in t. While for that closest to the DCP, γeff displays a sharp, nonmonotonic crossover from its nearly doubled 3D-Ising value toward its nearly doubled mean-field value with increase in t. The renormalized Ising regime extends over a relatively larger t range for the TL closest to the DCP, and a trend toward shrinkage in the renormalized Ising regime is observed as TL shifts away from the DCP. Nevertheless, the crossover to the mean-field limit extends well beyond t>10−2 for the TL’s studied. The observed crossover behavior is attributed to the presence of strong ion-induced clustering in this mixture, as revealed by various structure probing techniques. As far as the critical behavior in complex or associating mixtures with special critical points (like the DCP) is concerned, our results indicate that the influence of the DCP on the critical behavior must be taken into account not only on the renormalization of the critical exponent but also on the range of the Ising regime, which can shrink with decrease in the influence of the DCP and with the extent of structuring in the system. The utility of the field variable tUL in analyzing re-entrant phase transitions is demonstrated. The effective susceptibility exponent as a function of tUL displays a nonmonotonic crossover from its asymptotic 3D-Ising value toward a value slightly lower than its nonasymptotic mean-field value of 1. This behavior in the nonasymptotic, high tUL region is interpreted in terms of the possibility of a nonmonotonic crossover to the mean-field value from lower values, as foreseen earlier in micellar systems.

Voluntary Control of Multisaccade Gaze Shifts During Movement Preparation and Execution

Ramakrishnan A, Chokhandre S, Murthy A. Voluntary control of multisaccade gaze shifts during movement preparation and execution. J Neurophysiol 103: 2400-2416, 2010. First published February 17, 2010; doi: 10.1152/jn.00843.2009. Although the nature of gaze control regulating single saccades is relatively well documented, how such control is implemented to regulate multisaccade gaze shifts is not known. We used highly eccentric targets to elicit multisaccade gaze shifts and tested the ability of subjects to control the saccade sequence by presenting a second target on random trials. Their response allowed us to test the nature of control at many levels: before, during, and between saccades. Although the saccade sequence could be inhibited before it began, we observed clear signs of truncation of the first saccade, which confirmed that it could be inhibited in midflight as well. Using a race model that explains the control of single saccades, we estimated that it took about 100 ms to inhibit a planned saccade but took about 150 ms to inhibit a saccade during its execution. Although the time taken to inhibit was different, the high subject-wise correlation suggests a unitary inhibitory control acting at different levels in the oculomotor system. We also frequently observed responses that consisted of hypometric initial saccades, followed by secondary saccades to the initial target. Given the estimates of the inhibitory process provided by the model that also took into account the variances of the processes as well, the secondary saccades (average latency similar to 215 ms) should have been inhibited. Failure to inhibit the secondary saccade suggests that the intersaccadic interval in a multisaccade response is a ballistic stage. Collectively, these data indicate that the oculomotor system can control a response until a very late stage in its execution. However, if the response consists of multiple movements then the preparation of the second movement becomes refractory to new visual input, either because it is part of a preprogrammed sequence or as a consequence of being a corrective response to a motor error.

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.