In body ownership illusions participants feel that a mannequin or virtual body (VB) is their own. Earlier results suggest that body ownership over a body seen from behind in extra personal space is possible when the surrogate body is visually stroked and tapped on its back, while spatially and temporal synchronous tactile stimulation is applied to the participant's back. This result has been disputed with the claim that the results can be explained by self-recognition rather than somatic body ownership. We carried out an experiment with 30 participants in a between-groups design. They all saw the back of a VB 1.2 m in front, that moved in real-time determined by upper body motion capture. All felt tactile stimulation on their back, and for 15 of them this was spatially and temporally synchronous with stimulation that they saw on the back of the VB, but asynchronous for the other 15. After 3 min a revolving fan above the VB descended and stopped at the position of the VB neck. A questionnaire assessed referral of touch to the VB, body ownership, the illusion of drifting forwards toward the VB, and the VB drifting backwards. Heart rate deceleration (HRD) and the amount of head movement during the threat period were used to assess the response to the threat from the fan. Results showed that although referral of touch was significantly greater in the synchronous condition than the asynchronous, there were no other differences between the conditions. However, a further multivariate analysis revealed that in the visuotactile synchronous condition HRD and head movement increased with the illusion of forward drift and decreased with backwards drift. Body ownership contributed positively to these drift sensations. Our conclusion is that the setup results in a contradiction—somatic feelings associated with a distant body—that the brain attempts to resolve by generating drift illusions that would make the two bodies coincide. Is it possible to feel that a body you see in extra personal space is actually your body? The answer is obviously ‘yes’ - for it could be a mirror reflection, or a live video stream of your actual body. Suppose though that it is another body that is not in a mirror or a video, but a life-sized, three dimensional body that can be seen in your spatial surroundings a few meters away from your viewpoint: under what circumstances could this be felt to be your body? This issue has received attention in the cognitive neuroscience literature on body representation, concerned with how the brain represents the body. There are two different views—one suggesting that body ownership over a distant body is possible, and another that it is not. In this paper we describe an experiment that provides a unifying interpretation of the disparate results in this area, suggesting that both views are supportable.Inspired by the multisensory technique used in the rubber hand illusion  was seen on the back of the body image in front. Alternatively there was tapping on the chest (Chest) producing tactile stimulation while there was visual-only tapping at the place near the camera corresponding to the location of the hypothesized chest seen from that viewpoint. When the tapping was synchronous then in condition Back subjects would virtually have moved down toward the body below, while Chest subjects would have the illusion of being above the location of their real body . In Back subjects tended to affirm the statement that the body in front was theirs, but not so in Chest. Subjects had to imagine dropping a ball, and indicate the moment that they thought it would reach the floor. In the Back condition the imagined time to reach the floor was less than in the Chest condition.An experimental setup that combined these two paradigms was presented in Lenggenhager et al. . SubjectThe results of that paper suggest therefore that the critical element is where the visual tapping is seen (and correspondingly felt—the back or the chest). If it seen on the back of the body in front, and integrated through synchrony with the felt tapping, then an illusion of ownership over the body in front can occur, together with a drift toward that body. On the other hand when the visual tapping is seen at the position of the camera behind (and felt on the chest), then there is disownership of the body in front, and the sense of self-location is toward the position of the camera. The visual location of the tapping therefore plays a critical role—provided that the tactile stimulation is synchronous; it integrates the tactile with the visual tapping location to produce a congruent illusion that the body is where the tapping is seen.Back setup (avatar tapping seen on the back) there is no somatic illusion of body ownership over the distant body, but that the results can be explained through self recognition (indeed even the mannequin wore clothing similar to that of the participant). They claim that first person perspective (1PP) with respect to the surrogate body is an essential aspect of a somatic full body ownership illusion. Some evidence for this is provided in Slater et al. ? In Petkova et al.  it was ar et al. , Masellir et al.  where, ar et al.  there weIn this paper we replicate a version of the original experiment described in Lenggenhager et al.  except tThe experimental design was single binary factor between-groups with 30 male participants, each assigned to one of the two groups according to a pre-computed pseudo-random sequenceAll participants saw in virtual reality the full body of a male human character (or avatar) 1.2 m in front of their own position. The character was facing away from the participant Figure . A virtuth percentile 3.7 on a scale of 1–7 with 1 meaning no experience and 7 great experience).The two groups were comparable in their background. The mean ± S.E. age was 30 ± 1.7 in the Sync group and 28 ± 1.2 in the Async group. Based on a pre-experiment questionnaire there were nowhere near significant differences in their level of background computer knowledge, computer programming experience, prior experience of virtual reality, and computer game playing. In particular their prior experience of virtual reality was low  being tapped (the tapping object was away from the destination point). Actuators were turned on 100 ms after there was visual contact between the tapping object and the surface receiving tapping, and for a random duration between 150 and 350 ms. Random values used in our system were obtained using the On arrival at the laboratory participants completed a pre-questionnaire that recorded basic information . Participants also read an information sheet about the experiment and were invited to complete the informed consent form.Then the experimenter helped participants to place the ECG electrodes and put on the actuated haptic vest and make sure that it fitted tightly to the torso. The experimenter tested that both the Nexus-4 device to measure ECG and the haptic vest were able to communicate with the XVR application as expected. Also, tests were carried out in order to make sure that participants could sense the actuators from the vest.The experimenter briefed participants with precise instructions about the duration of the experiment, available affordances in the VR system, range of movements and how to act during the several stages of the VR experience. No information was given in advance regarding the actual content of the virtual environment. Participants were encouraged to ask any questions they had about the experiment before proceeding. They were also reminded that they could withdraw from the experiment at any time without giving any reasons.After this briefing, the experimenter attached two OptiTrack tracking devices to participants' wrists to register the arm movement. The participant then donned the HMD, which was fitted with the InterSense tracker, and adjustments were made to the HMD to ensure a correct stereoscopic view. Finally, they put on a pair of headphones so that they would hear some soft music with the purpose of avoiding distractions from external noises during the experiment.Just before starting the experiment, the XVR application required a calibration step to correctly register the relationship between the virtual head and arms and the participant's body. Then the experiment started, and participants were asked to look around to become familiar with the virtual environment and to move their upper body at will . After 3 min of this, a small virtual ball appeared in the participants' field of view and tapped the avatar body on its back. During that time, subjects were told to remain still and focus on the ball movements. The tapping continued for 3 min.Then participants experienced an unexpected event. There was a spinning fan in the room and it descended progressively (over 10 s) from the ceiling to the neck level of the avatar standing in front of the participants' point of view in the virtual environment. This followed a similar paradigm to Gonzalez-Franco et al. .After completion of the experiment they answered a post-questionnaire. Finally, participants were paid 10€ for their time.The post-questionnaire consisted of 9 questions shown in Table Heart rate deceleration (HRD) was computed for (i) 6 s before the fan started to descend as a baseline (HRD1) and (ii) for 6 s starting from 2 s before the fan finally stopped. This timing was based on interviews with participants that estimated the moment from when they actually saw the fan descending. HRD has been previously shown to be a response variable that significantly correlates with states of stress and anxiety induced by sudden unpleasant stimuli , and 10 s during the threat starting from 2 s after the fan started to descend (d2).For analysis of the questionnaire data as response variables we used the non-parametric Wilcoxon rank-sum test to test the difference between the conditions . To test whether the condition influenced the HRD and distance data we used ANCOVA with d2 and HRD2 as the respective dependent variables, condition  as the factor and d1 and HRD1 as the covariate. To examine whether the physiological and distance variables related to the questionnaire responses we used regression analysis.www.stata.com).All of the above are single equation techniques, meaning that we are unable to unravel more complex  simultaneous multivariate relationships between the variables. For example, a feeling of body ownership might simultaneously influence the physiological response to the threat (HRD2) and the distance that the head moved (d2), but these simultaneously are influenced by how much the participant tends anyway to move the head (d1) and have heart rate decelerations (HRD1). Conventional approaches have to separate these into separate stochastic linear models  that cannot assess multiple simultaneous effects. For this purpose we turned to path analysis, for example Kaplan, , where sThe questionnaire results are shown in Table There is no evidence for strong body ownership (Q3), both median scores are at the mid-point of the scale and there is no significant difference between them, however the distributions of scores are not the same with the majority of scores at the mid-point of 3 in the Async condition Figure .The control questions Q4–Q8 are as would be expected—low median scores with no significant difference between the Sync and Async conditions. Finally the same is true for Q9.F = 0.00, P > 0.98], and for the main effect without the interaction term F = 2.28, P >0.14). So although the descending fan had an effect on head movement this does not seem to be affected by the condition.Table F = 1.33, P > 0.25, and the main effect without including the interaction has F = 0.72, P > 0.40.Table Considering the results so far we find little support for the conclusions reached in Lenggenhager et al. . AlthougThis conclusion moreover is not too out of line with that of Lenggenhager et al.  with resThe other issue in relation to Lenggenhager et al.  is that We carried out a regression analysis of d2 on d1, condition, Q3, Q4 and Q7 allowing for interactions between condition and the other variables. After removing all non-significant interaction effects and main effects not associated with significant interaction effects, we arrive at the result shown in Table Table Hence overall the evidence suggests that the feeling of moving forward was associated with a greater response to the threat indicated by more head movements and higher HRD, and the feeling that the VB was moving backwards was associated with a diminution of HRD and head distance movement.One problem with the above analysis is that there are individual equations for d2 and HRD2, whereas the feelings represented by Q4 and Q7 may simultaneously affect both HRD and head movement. Moreover the role of Q3 (My Body) might be considered not as directly influencing HRD but mediated through its influence on Q4 and Q7. It would be interesting to consider these relationships together in one overall model, for which we turn to path analysis. Path analysis is a special case of Structural Equation Modeling (SEM) restricted to models that include only observed exogenous and endogenous variables, but not latent variables. A path model can be thought of as a set of simultaneous stochastic equations, where a dependent variable of one equation can be an independent variable in another. Based on any model specification  the overall covariance matrix is estimated, typically through maximum likelihood estimation. The standard general linear model  can be considered as a special case restricted to the situation where there is only one dependent variable . Path analysis was invented in the 1920s Wright,  and see Path analysis and more generally SEM can be used either for confirmatory analysis (to test a specific model hypothesis) or for exploration. Here we employ path analysis as an exploratory tool, to generate new hypotheses that arose due to the experiment, for testing in later studies.Our basic path model is based on the idea that the illusion of body ownership (Q3) should drive the illusions of moving forward (Q4) and that the avatar is moving backwards (Q7) (see Discussion). These in turn may be associated with changes in HRD and head distance.Figure yi is the ith observation on an ordered variable with possible values 1,2,…,q, and ηi = ∑ms = 1βsxis is the ith observation on a linear predictor for m independent or explanatory variables x1,… xm then the ordered logistic model is given by P denotes probability. The kj, j = 1, …, q, are ‘cut points’ with kq = ∞. The coefficients βs and the cut points are typically estimated by maximum likelihood.Q4 and Q7 are also endogenous variables but of a different type. Since these are ordinal they should not be modeled as continuous random variables, but rather we use an ordered logistic model. Here if 2(5) = 19.08, P < 0.002, showing a great improvement in the fit. Moreover the AIC (Akaike Information Criterion) reduces from 282 in the baseline model to 273 in the second model. If further terms are added  then there is no further gain in goodness of fit or notable reduction in AIC (but see Discussion). Table Figure 2 = 19.08,We have carried out a partial replication of the experiment described in Lenggenhager et al.  to examiHowever, a path analysis revealed results that are compatible with the earlier paper. The most striking is that HRD2 and d2 increase or decrease were associated with the illusion of drifting forwards (toward the danger) or the VB drifting backwards (away from the danger). The first of these can be interpreted as the participant illusorily entering into the danger zone, and the latter the VB moving out of it. The absolute median scores of Q4 (moving toward) and Q7 (avatar moving backwards) are similar to those in Lenggenhager et al.  on the sThe fact that these results do not clearly show up in the data, but only with a more sophisticated analysis are grounds for caution. In our experiment participants spent 3 min looking around the environment and moving their bodies during which the avatar in front carried out the same movements in synchrony  may be due simply to difficulty in obtaining a sensation of body ownership with respect to a remote body. There is evidence that body ownership illusion does not occur for a body that is in extrapersonal space when it is directly compared to a body that spatially coincides with the own body seen from 1PP. In Slater et al.  a full bIt was suggested in Petkova et al.  that an However, according to Q1 (Referred Touch) and Q2  there was feeling associated with the distant body. In these circumstances, therefore, the brain has a contradiction to resolve. There is evidence that is leading to the conclusion that your body is ‘over there,’ but also evidence  that points to you being ‘here.’ There is moreover a distinction between where you feel yourself to be (‘here’) and where your body might be (‘there’). Ways to resolve this contradiction are either to move yourself to ‘there’ (Q4 Drifting Forward) and/or to move the other body back toward you Q7 (Avatar Drifting Backwards). Each of these potential actions though has consequences in relation to the threat—the first making it more and the second making it less dangerous. Therefore the contradiction in the setup results in illusions of drift that are consequential for responses to the harm that might be caused by the descending fan. These illusions of drift are at least partially driven by the illusion of body ownership (Q3). While it may not be possible to have a somatic illusion of ownership over a distant body the brain attempts to resolve the contradiction through illusions of drift that would make, one way or another, the real and VB coincide. This mechanism does not contradict either standpoints mentioned in the introduction to this paper: there is an attempt by the brain, through drift, to make the distant body ‘owned’. Of course in direct comparisons between 1PP and 3PP the evidence suggests that 1PP results in the stronger illusion, but when the type of 3PP setup is considered by itself, it is still possible for participants to validly affirm a body ownership illusion over the distant body, but this could reflect more a process of attempting to resolve the contradiction between the feelings seemingly associated with the remote body, and the sense of self location at the actual position of the real body.Table Moreover, Table P = 0.12; synchronous condition: ρ = 0.60, P = 0.02; Q3 and Q7, asynchronous condition: ρ = 0.14, P = 0.63; synchronous condition: ρ = 0.69, P = 0.004). Including condition  and the interaction term Sync.Q3 in the path analysis as contributing to each of Q4 and Q7, the path from Sync.Q3 significantly and positively contributes to Q7 (P = 0.046) with no other changes to the results. Comparing this new model  with the previous model shown in Figure 2(2) = 6.05, P = 0.046). The evidence does suggest therefore that something additional is occurring in the synchronous condition. In that condition the model indicates that the level of ownership drives Q4 and Q7, and that it is these illusions that are contributing to HRD and the head movement distance over and above what might normally occur when seeing a threat to any body. In other words ownership plays a critical role (but clearly not an exclusive one).Considering the relationships between Q4 and Q3, and between Q7 and Q3 by themselves the correlations between them are only significant in the synchronous condition (Q3 and Q4, asynchronous condition: Spearman's ρ = 0.42, The results of this experiment, and the exploratory path analysis, produce quite an interesting set of findings. However, it is important to note that given the limitations of the study discussed above, that these are taken only as hypotheses to be rigorously tested in future work.The experiment was conceived by Mel Slater and designed by Mel Slater and Ausiàs Pomés. The implementation and experiment were carried out by Ausiàs Pomés. The analysis of results was carried out by Mel Slater, and the paper written by Mel Slater in conjunction with Ausiàs Pomés.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Life course epidemiology concentrates on the contribution that social or physical exposures have across the life course on adult health. It is known that the area of residence can affect health, but little is known about the effect of the area of residence across the life course. We examine the contribution that area of residence in 1960, 1970, 1980 and 1990 made on subsequent mortality for 49736 male inhabitants of Oslo in 1990. We compare the performance of multiple-membership and cross-classified multilevel models on these data with a correlated cross-classified model that was developed for this. A recent focus of chronic disease epidemiology has been in how exposures across the whole life course may influence health in adult life . Variousper se but rather a combination of region  and type of area. Chandola et al. (2005) examined the influence of area of residence between 1991 and 1998—yearly—on physical and mental health functioning in 1999. They used a multiple-membership multilevel model with area defined by electoral wards—fairly small areas containing between one and 10 households in the sample that was used. A large body of literature exists examining the relationship between the place of residence and health and the reasons why such a relationship may exist. Environmental influences on health extend beyond the obvious physical factors such as a lack of clean water or exposure to pollutants  to socioWe are interested in reanalysing the Oslo mortality study data with a view to determining the extent to which the area of residence at different stages of the life course impacts on subsequent mortality. So for someone who was aged between 30 and 39 years in 1990 we want to ascertain the relative importance of the area of residence in each of 1960 (aged 0–9 years), 1970 (aged 10–19 years), 1980 (aged 20–29 years) and 1990. If we can estimate a variance that is associated with the area of residence at each time point then we can partition the total variance due to area of residence (at these four times) into that attributable to each time point. Multilevel models are commonly used to partition variance and there is a clear hierarchical structure to the data, with individuals living in one area at each time. If we find one time point to be more important than the others—i.e. it is associated with a larger variance—then there is a suggestion that this is a critical period for contextual influences on development. If, in contrast, we find a suggestion that all time points are of equal importance then we can view this as some evidence that risk is being accumulated across the life course.There remains a question about what model is suitable for the analysis of the effect of area over the life course. The two previously used approaches—multiple-membership models and cross-classified models—make different assumptions about how the effect of an area on individual health changes over time. Both models have their disadvantages. In this paper we describe the data set and then detail various models that could be used to model the data. In particular, we consider simple hierarchical models that use information from area of residence at just one time point, multiple-membership models and cross-classified models. We also show how the multiple-membership model can be extended for such data to enable empirical estimation of the importance that is attached to an area at each time point, and how multiple-membership models and cross-classified models can be combined to allow correlations between areas over time to vary between 0 and 1. We then present the results of fitting these models to the data and finish by drawing some conclusions about the use of such models in epidemiological research, as well as drawing substantive conclusions regarding these data.n=49 736) had an age-adjusted mortality rate of 111 (per 10000 person-years).Census information from 1960, 1970, 1980 and 1990 was linked for individuals to the death register (including deaths from 1990 to 1998). The study population was all male inhabitants of Oslo on January 1st, 1990, who were aged 30–69 years: a total of 122951 individuals. There were relatively few deaths among women in the younger age groups and we have restricted our analysis to men. To study the residential history of people in Oslo, only those who had been resident at all four censuses were included: a total of 50860 men. Immigrants to Oslo during this period had an age-adjusted mortality rate of 101 (per 10000 person-years). Of the cohort selected, people with missing data on area of residence at any of the censuses were excluded—a total of 1124 individuals with an age-adjusted mortality rate of 211 (per 10000 person-years). The remaining included population ; the same percentage of the cohort of those aged 40–49 years in 1990 migrated between the 1970 and 1980 censuses. Of those aged 50–59 years in 1990, 68% migrated between the 1960 and 1970 censuses. Migration levels then decreased as those in each cohort aged; the lowest migration level (15%) was seen between the 1980 and 1990 censuses for those aged 60–69 years in 1990. The lower level of migration means that in this cohort there will be less power to detect differences between the effect of place of residence in 1980 and 1990. The median size of population in each area decreased over time with a corresponding increase in heterogeneity of size (as measured by the standard deviation of the populations). Areas with different sizes had similar age-adjusted mortality at each time point. More detail of the data is provided elsewhere (We illustrate the format of the data in n=12 529), 40–49 years (n=11 357), 50–59 years (n=9967) and 60–69 years (n=15 883). The four cohorts were analysed separately. The mean population in each area ranged from 144 for those aged 50–59 years to 230 at ages 60–69 years. Differences in the size of the study population in each age group—including the potentially surprising finding that the population is larger for those aged 60–69 years in 1990 than for any of the other age groups—reflects a combination of differences in the size of the original birth cohorts, differential probabilities of migration out of Oslo and different survival probabilities into the age of follow-up. The outcome that was considered was death at any stage during the follow-up. The response that was used was therefore binary . Model estimation was by Bayesian Markov chain Monte Carlo sampling, necessitating the specification of prior distributions on parameters (see Section 4). All models were fitted using WinBUGS version 1.4.1 (The data related to men in Oslo and were broken down into four cohorts according to age in 1990: those aged 30–39 years (i lived by area60(i) in 1960, area70(i) in 1970, area80(i) in 1980 and area90(i) in 1990. So for person 1 in yi for individual i, i.e.We model the probability of death at any stage during the follow-up period from 1990 to 1998; mortality is sufficiently rare in all four cohorts for the odds ratios to approximate hazard ratios. We consider several ways of modelling the data; in this section we present the algebraic description of the models together with the strengths and weaknesses of each. The models that were considered come under the multiple-membership multiple-classification models that were developed by πi, related to a vector of characteristics i through a vector of fixed parameters β, and to the random effects denoting the area of residence at each census. We have restricted covariate information to two dummy variables indicating to which 5-year age group individual i belongs. For example, when modelling the 30–39 years cohort in 1990 we have a dummy variable xi0 which takes the value 1 if individual i was aged 30–34 years in 1990 and 0 otherwise, and a variable xi1=1−xi0 which takes the value 1 if individual i was aged 35–39 years in 1990 and 0 otherwise. We then have a vector of fixed parameters β=T. We assume a logit link from the probability i) in year YR on subsequent mortality. The full model can then be written as X={Xi} is the fixed part design matrix that is formed by stacking the individual characteristics Xi, U(YR) is the vector of the residuals for areas in year YR, j=1,…,J, and Z(YR) is the random-part design matrix that identifies the area in which an individual lived in year YR. The four residuals for any particular area j corresponding to the four different census years are assumed to have a joint normal distribution, with the exact composition of the dispersion matrix Σ of order 4 being what differentiates between the models that are presented below, We assume an area effect a priori uncorrelated, regardless of the year. This means that the residuals for areas 1 and 2, for example, would have a joint distribution given byNote that we still assume that the residuals for different areas are (60), for example, considers the effect of the area of residence in 1960 on subsequent mortality. We can rewrite We include the effect of the area of residence in a single year only. Model Aπi) that are implied by the various models for person 1 and person 5 in X’.)Throughout this section we illustrate the variances of logit=0.25 for each census. The number of distinct areas can range from 1 to 4. For example, from Multiple-membership models are used when an individual is simultaneously a member of more than one higher level unit. These models have been developed in an educational context in which pupils may receive their education from more than one school (see for example This can in turn be expressed in terms of 1(i)≠areaYR2(i) for two different census years YR1 and YR2 that are both elements of {60,70,80,90} then as in distribution (5) the covariance of f1(i)areaYR and f2(i)areaYR is 0. However, where areas are common to censuses we have areaYR1(i)=areaYR2(i), and random effects are possibly repeated, this covariance term is We also note that if areaYRj on mortality between 1990 and 1998 is assumed to be the same regardless of whether an individual lived in that area in 1960 or 1990, i.e. without regard to how the circumstances of the area might have changed or how the effect of an area may differ at different stages of the life course. Taking into account the absence of correlation between different areas, we can see that the variance arising from the area effects will differ according to the length of time that is spent in the same area. Returning to πi) for person 5 would be πi) for person 1 and person 5 that is induced by the fact that they both lived in area 1—person 1 at four censuses, and person 5 at one census—is given by This model makes the simplifying assumption that area effects are constant over time. This means that the effect of area The weighting scheme that is used for the multiple-membership model (model B) makes the assumption that the area of residence is of equal importance at all stages of the life course  for person 1 in This gives i lived in area areaYR(i) in year YR and is 0 otherwise. This ensures that the weights for each individual sum to 1 as in πi) from YR1≠YR2) ∈ {60,70,80,90}. Writing For person 5 the variance is Cross-classified models are used when there is no strict hierarchical structure to higher level units . Such moThis model is distinguished from the unconstrained multiple-membership model—model C—by the assumption that the residuals are independent. So we have πi) is For both person 1 and person 5 in πi) for person 1 in We can combine the cross-classified model D and the unconstrained multiple-membership model C such that there will be correlations between areas at different time points. These correlations are induced by the assumed perfectly correlated effects of areas (from the multiple-membership model), which are additional to independent (uncorrelated) area effects (from the cross-classified model). Substantively, this model can be thought of as combining constant area effects that vary in magnitude according to the year or stage of the life course with area effects that represent the ways in which areas change over time (and are therefore uncorrelated). We now write Σ—the eight variances—since specification of these will determine the covariances. This compares with 10 parameters in the full multivariate model (see below). The potential gain in efficiency (through fewer parameters) comes at the expense of the constraint that the correlations in Σ—i.e. the number of occasions on which we know where each individual lives—increases.For person 5 the variance is Finally, we consider a model in which we assume that the random effects have a full multivariate normal distribution. We adapt πi) is All the variances and covariances in this model are now freely estimated, subject to the usual constraints on a covariance matrix. For person 1 in For all models we assume flat (improper) priors for the fixed effects of age In general we assume uniform priors for the square root of the area variances; in this section we detail how these priors were operationalized. Throughout we have used uniform priors with a lower bound of 0 and an upper bound of 5; although not truly uninformative, the upper bound would correspond to a variance between areas of 25 on the log-odds scale. Assuming a threshold model, as described in σv(YR) to which we assign a uniform prior. For example for 1960 we have We assume a normal distribution for the area level residuals with standard deviation σf to which we assign a uniform prior: Again we assume a normal distribution for the area level residuals, this time with standard deviation N distribution for the area level residuals and scale these by multiplying by the appropriate standard deviation σf(YR). This ensures that the correlations between the effects for one area at two different times are constrained to be 1. The σf(YR) are assigned uniform priors: We assume a standard normal σv(YR) to which we assign a uniform prior: We assume a normal distribution for the area level residuals with standard deviation We use the prior specifications from Sections 4.3 and 4.4, combining the unconstrained multiple-membership model and the cross-classified model.Σ−1 to which we assign a Wishart distribution: The priors that were used in the multivariate normal model differ from the priors that were listed in Sections 4.1–4.5 as implemented in WinBUGS (Σ−1). We considered three specifications of the scale matrix R: I, the identity matrix, 0.1I and 0.4I. R can be thought of as an estimate of the order of magnitude of kΣ Σ. For the general multivariate model (model F) with Σ given by that the variances are the same for the movers and stayers (and for any other migration pattern). In models B, C and E the positive correlation between area effects at different times meant that the variances in the contribution of areas to mortality were higher among those who had lived in the same area at all four censuses  than among those who had moved, albeit such differences were small relative to the credible intervals. The negative correlations between area effects at different times that are seen in The variance partition coefficient is a commonly used means of expressing the proportion of the total variance that is attributable to each level of a multilevel model. A variety of methods of estimating the variance partition coefficient have been proposed  stage of the life course. The fit of the unconstrained multiple-membership model—as assessed by the DIC—proved similar to that for the cross-classified model. But, just as the cross-classified model makes the assumption that the area effects are uncorrelated over time, the unconstrained multiple-membership model still assumes that there is perfect correlation between area effects at one time point and another. The data suggested that area effects were positively correlated over time but with correlation less than 1. We have shown how such correlations between classifications can be modelled by combining the independent effects of the cross-classified model with the correlated effects of the (unconstrained) multiple-membership model. Such models have widespread potential as a modelling framework when repeated observations are made on the environment or context which influences individual outcomes.In this paper we have introduced an extension to the multiple-membership model by showing how weights may in effect be estimated empirically from the data as an alternative to an The differences between the results that were provided by the various models were not large and did not materially affect the substantive conclusions that we drew—namely that the most recent areas of residence  were most influential in determining mortality for the youngest ages cohorts aged 30–59 years in 1990 whereas the oldest ages cohort showed more evidence of having accumulated risk from areas of residence across the life course. These findings are consistent with earlier findings based on these data in which cause-specific analyses have shown that there is a cumulative effect across the life course for chronic diseases such as coronary heart disease, chronic obstructive lung disease and smoking-related cancers, which are more common at older ages, and a critical period effect of more recent circumstances for violent and psychiatric causes of death, which are more common at younger ages. Such findings held when either individual level socio-economic life course factors (


Quartz tuning forks are being increasingly employed as sensors in non-contact atomic force microscopy especially in the “qPlus” design. In this study a new and easily applicable setup has been used to determine the static spring constant at several positions along the prong of the tuning fork. The results show a significant deviation from values calculated with the beam formula. In order to understand this discrepancy the complete sensor set-up has been digitally rebuilt and analyzed by using finite element method simulations. These simulations provide a detailed view of the strain/stress distribution inside the tuning fork. The simulations show quantitative agreement with the beam formula if the beam origin is shifted to the position of zero stress onset inside the tuning fork base and torsional effects are also included. We further found significant discrepancies between experimental calibration values and predictions from the shifted beam formula, which are related to a large variance in tip misalignment during the tuning fork assembling process. Atomic force microscopy (AFM) allows the imaging of surfaces with true atomic resolution and the resolution of intra-molecular structures of molecules . FurtherkqPlus is crucial for quantitative interpretation of force spectroscopy measurements. Early spectroscopy experiments compared relative forces with high accuracy, for which the absolute stiffness of the sensor was not critical. Latest measurements of the absolute interaction forces impress by their force resolution [4f, to forces. Consequently, a force measurement can only be as precise as the determination of each factor in the equation that links the frequency shift to the tip–sample forces [kqPlus as prefactor and therefore directly suffer from an inaccurate determination of the spring constant.Common AFM sensors are microfabricated from silicon or silicon nitride with the tip already integrated. Their spread in geometric parameters is within a low range and the characterization of their geometric parameters has been presented extensively by theory and experiments –8. Quartsolution –49 but se forces –11. To ce forces  with higHere we present an experimental procedure that allows for the direct measurement of the stiffness of a tuning fork sensor in the “qPlus” design with standard lab equipment. Our results reveal that a large spread of stiffness exists even in a series of commercially sold sensors. This finding underpins the urge of the individual characterization of each sensor. The standard equation  to calculTF = 3548 μm and a height of hTF = 651.4 μm at the widest point while the substrate has a thickness giving the tuning forks width of wTF = 120.8 μm and a prong thickness of tTF = 207.3 μm. The quartz tuning fork, originally used as frequency normal in wrist watches constitutes the centerpiece of a force sensor in the “qPlus” design. kqPlus = 1800–2000 N/m are used for the force transformation. These values are estimated from the geometric dimensions of the free prong of the tuning fork and the Young’s modulus of quartz by using the beam formula according to Commonly, spring constants of w and t are the width and thickness of the free prong, respectively and Equartz is the Young’s modulus of quartz. The limitations for the validity of this formula are small deformations leading to only elastic stress/stain inside the uniform, rectangular cross section of the beam, which consists of isotropic material and is rigidly fixed at the end. These conditions are not necessarily fulfilled for a real tuning fork sensor. Since the tip wire is not necessarily placed at the very end of the prong, ΔL = L − L0 denotes the effective length of the free beam, i.e., the wire position L along the prong with respect to the beam origin L0. The comparison with L0. At the beam base the cross-section of the prong broadens before ending into the rigid basis. We here choose the point before the broadening as the zero point L0 as it is commonly done in the nc-AFM literature in order to avoid inaccuracies in later discussions. Inserting our measured values of ΔL1 = 2139 μm, w = 207.3 μm and t = 120.8 μm into Equartz = 78.7 GPa results in a stiffness of the free prong of kqPlus = 1898 N/m. This is within the range of reported spring constant values kqPlus = N/m [kqPlus = 2000 N/m [Equartz = 79.1 GPa to correct for the non-orthogonal crystallographic cut through the substrate of the tuning forks.In this equation us = N/m  and kqPlL cannot be regarded as constant for all sensors. The broadening of the beam towards the basis and the unknown Young’s modulus of the material limit the usage of the beam formula for the description of the tuning fork stiffness. Even influences of the glue, which is used to fix the tuning fork onto its holder, and the resulting spread in the individual stiffness of these sensors have recently been reported [However, the underlying models of these calculations are barely in agreement with the actual geometry of real “qPlus” sensors, in which the force is applied through a metal wire glued onto the free prong. Therefore, the force application point is defined by the position of the glue point. Since these sensors are handmade it is obvious that the length Δreported . Possiblreported  or statireported –18 of threported . Here wedW-wire = 50 μm was glued onto the free prong. This sensor is mounted onto a traverse, which can be lowered by a micrometer screw  with an accuracy of Δz = 5 μm. Below the moveable traverse, a scale is placed  with a mass resolution of Δm = 1 mg. The force applied to the scale is then calculated by multiplying the weight with the gravitation constant g = 9.81 m/s2 resulting in an accuracy of the force measurement of 9.81 μN. The stiffness of the sensor can now be measured by pushing the sensor onto the scale with the micrometer screw while simultaneously measuring the weight increase on the scale. By lowering the end of the wire into a fresh droplet of Torr Seal epoxy glue, it can be mechanically fixed onto a glass substrate resting on the scale , which was in our case ksetup = 5952 N/m. The stiffness of the tuning fork can then be evaluated by In order to validate this measurement method we assembled a test sensor similar to the “qPlus” sensor setup. In the same way as in a “qPlus” sensor, a quartz tuning fork was glued onto a Macor body, and a tungsten wire with a diameter of cale cf. , inset. L = L − L0 with respect to the force application point L. L values), the measurement seems to be roughly within the range of the calculation, for shorter prongs  a drastic discrepancy between the measured stiffness and the calculated value is found  resulting in a Young’s modulus ETorrSeal,RT = 4000 GPa. As our custom-build “qPlus” sensors are cured out in an oven, the value of ETorrSeal = 6000 GPa was used in our FEM simulations for the epoxy glue. The geometry of the simulated model is depicted in Special care was taken to make the geometric model of the “qPlus” sensor in the FEM software as realistic as possible, including gluing points as well as a metal tip. As for the tuning fork, an isotropic Young’s modulus of Fload = 1–100 mN, which results in a displacement of the very end of the free prong of xend = 50 μm. Since the tip was attached to the side of the tuning fork, as it is also the case in commercial “qPlus” sensors, the different stress contributions of torsional and normal stress are color coded as the comparative von Mises stress (σVMSmin). The color code represents stress values from σVMSmin = 0 N/m2 (red) to maximum values of σVMSmax = 2.5·108 N/m2 (violet). The area of onset of stress within the basis is marked by the dashed circle.In the next step a force was applied through the vertical axis of the wire and the displacement of the free prong was analyzed. Interestingly, a closer look at the stress distribution reveals that the stress is reaching several hundred microns into the basis of the tuning fork. L0, as origin for the length of the cantilever, has to be adjusted when calculating the stiffness of a tuning fork by using the simple beam formula. To demonstrate this effect we first plot the stiffness of the tuning fork in L0 = 0 as a reference curve. The logarithmic plot shows that the spring constant versus beam length curve (gray curves) does not follow a certain power law, e.g., ΔL−3 as expected from L0 + ΔL0 reaching into the base of the tuning fork. The resulting set of curves is plotted in the diagram of L0 was adjusted to a range from 350 μm to −750 μm. Here, in the transition regime between the two extreme L0 positions, a linear behavior can be identified at an effective origin of L0 = −250 μm, which is located “inside” the basis of the tuning fork with respect to the initial origin at L0 = 0. For the new origin L0 = −250 μm we find quantitative agreement between simulations and beam formula for larger tip wire positions ΔL > 1500 μm, which is the case in conventional “qPlus” sensors but also indicates that additional care has to be taken when working with shorter prongs. Only if the tip wire is closer to the basis, some deviations occur, in which the beam formula is systematically overestimating the stiffness. Therefore we conclude that the beam formula can still be used to estimate the tuning fork prong spring constant, if the beam origin is set to the new effective position L0 = −250 μm (for the tuning forks used here) and if the tip wire position is more than 1500 μm away from the origin.This finding suggests that the zero point In the following, the still existing deviation between the FEM results and the beam formula, is subject to further investigations. Therefore we simplify our experimental and FEM setup. To eliminate a possible influence caused by the tip, we carried out two separate measurement series to determine the spring constant directly by applying a force onto the top of a tuning fork sensor prong, together with an analogue FEM simulation. The experimental setup and the corresponding results are displayed by the graph and the photograph in Subsequently we investigate the influence of torsional motion of the tuning fork prong, which may also play an important role. While the beam formula only considers normal forces applied orthogonal to the axis of the prong, in the “qPlus” sensor configuration, the wire-tip is attached at the side causing a torque around the axis of the beam in addition to the bending of the prong. To evaluate the influence of the torsion, the simulation was repeated with the tip positioned at the center of the prong . In our FEM simulations the position was chosen with the tip on the top of the prong (TOT), allowing us to vary the position of the force application point, for direct comparison to the results from the tip on side (TOS) configuration, which was discussed so far. T is the torsional momentum, Φt is the angle of twist in radians, L the length at which the force is applied, G the shear momentum and IT the second momentum of area of the prong. To calculate the exact influence of the torsion to the overall spring constant, the tuning fork has to be seen as a system of two springs (deflection and torsion) connected in series. The red curve in the diagram shows the result from the simulated TOT-configuration where the effect of the torsion is corrected with the above equation. The torsion corrected curve coincides well with the curve simulated for the TOS configuration of the “qPlus” sensor. These results also demonstrate that torsion has a negligible influence at the free end of the prong, since the torsion spring constant is decreasing linearly whereas the deflection spring constant decreases with ΔL−3. Only if the tip is mounted closer to the origin of the tuning fork body, the torsion has an increasing influence on the overall spring constant. This influence results in a smaller increase of the overall spring constant as the torsion spring constant is not increasing as fast as the deflection spring constant. This effect is obvious in the area of smaller ΔL-values, in which the TOS curve shows a recognizably lower spring constant, than the TOT-curve.in which Before we proceed by finally comparing the results of the FEM calculations and the modified beam formula with the experimental spring constants, we consider one further important issue related to the hand-made “qPlus” sensor fabrication. Since the wire is glued on the prong, very often a small tilt of the wire long axis with respect to the prong surface normal cannot be excluded. Unfortunately, the torsion caused by the non central fixation of the tungsten wire is increasing, when the wire is not perpendicular mounted to the tuning fork. Therefore we conducted further FEM simulations considering a possible wire axis tilt, with the results shown in L values (ΔL > 1500 μm) the agreement between experiment and simulations/beam formula is acceptable, if the shifted origin method is applied. Please note that the scatter between the individual experimental data points is larger than the difference between beam formula and FEM data with 5° tilt angle.As the final step, L > 1500 μm. Still in this case a typical error of about 50% remains, which is mainly due to angular misalignment effects during the tip wire fixation to the free prong. For more precise spring constant determination, as required for quantitative force spectroscopy experiments, individual calibration of the used tuning fork sensors after the nc-AFM experiment is mandatory.From this section we conclude that using the conventional beam formula for the calculation of the spring constants of tuning forks results in a dramatic overestimation of the beam compliance. However, the origin shifted beam formula can be used to estimate the “qPlus” spring constant for Δx0 = −250 μm into the basis. This length can either be measured from SEM images of tuning fork sensors or even simpler by microscopic photograph. However, the present study reveals that the stiffness of real sensors can differ from the simulations due to deviations between the real tuning fork tip alignment and the ideal FEM model geometry. Whenever a more precise value of the static spring constant is required, due to the significantly large spread of the experimental results, the presented method to measure the stiffness directly can be applied to the sensor after the AFM spectroscopy experiment.A simple method for measuring the spring constant of tuning fork sensors using a micrometer screw and a scale is presented. The experimental results are compared to the beam formula and FEM-simulations revealing the limits of the commonly used models for the determination of “qPlus” sensor stiffness. The combination of finite element method simulation with experimental measurements allows a comprehensive understanding of the spring constant behavior alongside the whole length of the free prong. This knowledge finally opens the opportunity to adapt the beam formula by shifting the origin of the beam formula and thus making it a reliable tool for the spring constant determination in the area around the last millimeter of the prong. Since the beam formula is calibrated by the present study, it can be used for the determination of spring constants of “qPlus” sensors by measuring the effective length between the force application point at the gluing droplet attaching the wire to the prong and the shifted coordinate for the zero point of Δ


Bacterial genomes exhibit a remarkable degree of variation in the presence and absence of genes, which probably extends to the level of individual pathways. This variation may be a consequence of the significant evolutionary role played by horizontal gene transfer, but might also be explained by the loss of genes through mutation. A challenge is to understand why there would be variation in gene presence within pathways if they confer a benefit only when complete.Here, we develop a mathematical model to study how variation in pathway content is produced by horizontal transfer, gene loss and partial exposure of a population to a novel environment.We discuss the possibility that variation in gene presence acts as cryptic genetic variation on which selection acts when the appropriate environment occurs. We find that a high level of variation in gene presence can be readily explained by decay of the pathway through mutation when there is no longer exposure to the selective environment, or when selection becomes too weak to maintain the genes. In the context of pathway variation the role of horizontal gene transfer is probably the initial introduction of a complete novel pathway rather than in building up the variation in a genome without the pathway. Escherichia coli studied by Welch et al. 2002.The metabolic cost of carrying genes is likely to be low, so we cx is a state vector x = T, and A is the matrix whose  entry is given by the coefficient of xj in the expansion ofnon-linear system, sincex.This system has a unique equilibrium, as the following shows. The state transitions of this model can be described by the equationA in the light of the Perron-Frobenius Theorem for irreducible matrices  eigenvalue is the spectral radius of the matrix and is called the Perron root, and the positive eigenvector is called the Perron vector.Despite the system’s non-linearity, we can obtain the existence and uniqueness of an equilibrium state through considering the matrix example,). This Tn + 1)×(n + 1)matrix A that arises in our model is irreducible because it is regular, meaning that a positive power of A has strictly positive entries. This in turn follows because the entries of A are all strictly positive on and below the main diagonal, as well as in the first diagonal above the main diagonal (the remaining entries are zero). Hence An will have only positive entries, implying that A is regular. The Perron-Frobenius Theorem therefore applies, and so A has a unique eigenvector that is a scalar multiple of a positive vector. In other words, there is an eigenvector of A that consists of positive entries, and with the additional constraint that the entries sum to 1 this vector  is unique. In concrete terms, there is a unique positive vector v summing to 1 such that Av = λv, with λ > 0. This provides a unique solution to our system’s equilibrium equationx is the Perron vector v andλ.The  or fixed on the empty pathway (x0 high). The cost c favours the empty state while exposure εfavours the full pathway, and the balance between these two factors is seen by comparing the fitnesses of the two extreme states. The separation between high x0and high xn should occur when wn=1=w0which holds when A consideration of the fitnesses reveals conditions under which the population is closer to being either fixed on the complete pathway (wi (Equation (1)). That is, under this heuristic, when ε > ε∗ the dynamics should move to high values of xnat equilibrium. Note that for a given fitness cost c, as the pathway length n increases the exposure ε required in order for the pathway to become fixed in the population also increases.following from the definition of x0=1), and 2. All individuals in the population carried all of the pathway . We use these initial conditions to understand how genes of a pathway are acquired and lost; other initial conditions would also lead to the unique internal equilibrium point described above.We study the transient dynamics of pathway acquisition numerically by setting the parameters according to Tablen + 1)-dimensional space is by compressing some coordinates and using a de Finetti diagram  as foll gives the proportion of the population with at least one of the genes, but not the complete pathway, and this reflects the extent of variation in gene content in the pathway. Figureγ1 of transfer of a single gene and the extent of clustering κ, while selection is controlled by c, b and ε.To study how the dynamics of this system are affected by horizontal transfer and natural selection, we varied parameters controlling these features of the model  as exposure increases. The overall appearance of the dynamics is similar for high and low transfer settings, even though the base transfer rates differ by six orders of magnitude. The equilibrium is more polymorphic in the case of the high transfer rate.Figureγ1), and low and high clustering (modelled by κ), but consider all four scenarios . We allowed c to vary between 0 and 0.01, and ε to vary between 0 and 1, dividing each parameter range into nine values (eight non-zero). The output quantities of interest here are the equilibrium point and the extent of variation in pathway content. The equilibrium point tells us whether the full pathway or the empty pathway is fixed or nearly fixed in the population, or if there is notable variation in the population at equilibrium. The extent of variation in gene content generated in the trajectory is captured by the peak variation (1 − x0 − xn) during the dynamics.We further characterised transfer and selection as follows. As before we examine low and high transfer rates , the full pathway is acquired by over 95% of the population (indicated by a black shape). If the transfer rate is low (panels C and D), we do not have 95% of the equilibrium population at either the full or empty pathway (indicated by a greyed shape).The first question to ask of this model is how it behaves in the absence of any cost to carrying a partial pathway and no benefit from the acquisition of the full pathway. In this way the impact of the transfer dynamics is isolated. Since we have fixed the benefit −9, and so when the transfer rate is of a similar order of magnitude γ1 = 10−9(regardless of κ), as in the lower panels, equilibrium is near neither “corner” (x0 = 1or xn = 1). In the case of a higher transfer rate  and deletion (pushing away). The deletion rate is fixed at 10γ1 and high κ). In this case, variation at equilibrium appears in a wider range of parameter values.The predicted threshold given by Equation (3), shown as a dashed curve on Figurex0 − xn is an indicator of this variation. On the de Finetti diagram of a given trajectory  is also high . A second threshold exposure derives from this argument, namely at ε∗∗ but still lower than ε∗, selection leads to pathway decay but through a more direct replacement with the empty pathway. The threshold given in Equation (4) corresponds to a very low level of exposure, closer to the far left column of the panels in Figureε=0.125). Figureε∗∗ = 0.039 for these parameters lying between the second and third columns.Roughly speaking, for exposure levels lower than this, large amounts of variation in gene presence appear as pathways decay. When exposure levels are higher than Equation  correspoε = 0) — the left columns of each panel in FigureWhen there is no exposure to the selective environment at all . In the extreme case, when n = 1, there are only two states in the system, presence or absence of the pathway. Consequently there is no “variation” in gene presence in the sense of there being partial pathways. However the equilibrium behaviour can be established. Because there are only two coupled states, the system reduces to a quadratic in one variable, namely We varied the length of the pathway to study the effect of this parameter on the model behaviour. To cover realistic pathway lengths we explored a wide range of values , we have both states equally fit (w0 = w1 = 1), and the system becomes linear. The dynamics are then a balance between transfer γ1 and deletion δ, and the equilibrium is simply x0 = δ/(δ + γ1) and x1 = γ1/(δ + γ1). If deletion and transfer occur at the same rate, the equilibrium is  = .In the light of the discussion of the equilibrium above, exactly one of these gives a positive solution for n>1 pathway acquisition requires more exposure to the beneficial environment, relative to fitness cost. That is, the pathway acquisition threshold ε∗(Equation (3)) moves to the right as shown in Figurec fixed but varying exposure ε in both high and low transfer scenarios. The immediate observation is that variation is more common with longer pathways, as might be expected. It is also clear that this variation occurs in the course of pathway loss (indicated by unfilled circles in Figuren and acquisition behaviour as εincreases. With low n and high transfer (top row, Figureγ1 and the deletion rate 10−9gives rise to variation en route to an equilibrium with the full pathway or in between. The slight difference in acquisition behaviour between high and low transfer rates over various n concurs with the difference seen in FigureFor Analysis of the model shows that with continuous partial exposure to the selective environment a pathway can be acquired when the level of exposure is high enough compared to the cost of carrying fragments of the pathway. Continuous partial exposure may explain, for instance, the acquisition of porphyranase genes from marine bacteria by human gut bacteria. From the perspective of the gut microbes, the diet of humans ingesting seaweed provides constant exposure to the selective environment containing polysaccharides that marine bacteria are able to metabolise. Because genes of a pathway are often clustered on chromosomes,24, horicryptic genetic variation, or evolutionary capacitance, which is usually discussed in the context of eukaryotes[cryptic genes in the sense of Hall et al. 1983[We have shown that some variation in the presence of genes of the pathway can accumulate when the selective environment is absent, or nearly absent, in certain conditions. Such variation is seen in Figurekaryotes-28. In pal. 1983 who haveVarious genetic structures and mechanisms promote the transfer of genes between bacterial genomes. Integrons, for example, capture genes in cassette structures and are notable for their role, in conjunction with plasmids, in the accumulation of multiple drug resistance genes in pathogens,30. HereShigella[Mycobacterium leprae[Our model shows how variation in gene presence can also occur through decay of an existing pathway. This type of variation occurs when exposure is very low or zero; that is, when the selective environment no longer acts on the pathway. Here, the pathway is mostly lost at equilibrium but there is a large degree of variation produced transiently as the pathway decays. This variation in gene content is generally far greater than the variation due to the accumulation of genes by horizontal transfer Figure. The modShigella,33 and Mum leprae is a cleHorizontal gene transfer has frequently been argued to be an important force in bacterial genome evolution. This stAs more genomic data become available, a careful examination of variation within pathways within species will shed light on these ideas. If the distribution of the number of genes in a pathway is either weighted towards the complete pathway or weighted in the middle (e.g., FigureAnalysis of the mathematical model developed in this study has shown that a high level of variation in gene presence in bacterial genomes can be readily explained through decay of an existing pathway. In the context of pathway variation the role of horizontal gene transfer is probably the initial introduction of a complete novel pathway rather than in building up the variation in a genome without the pathway.ARF and MMT designed the study, performed the research, and wrote the manuscript. Both authors read and approved the final manuscript.


Schemes for optimizing ocean observation programs are presently the subject of increased interest since in principle they should lead to the improved understanding of the dynamical state of the ocean that is required within the present regime of climate change. Here we use an adjoint sensitivity analysis together with a four-dimensional fluctuating oceanic current system to identify key regions for intensive monitoring by drifting profiling float. In this way we aim to maximize observational efficiency. As a scientific benchmark for the validity of our approach, we have attempted to define the ambient sensitivity of the oceanic heat content to a subtle change in water temperature within the Pacific Basin. We focus on the interannual to multidecadal variations in particular. As a result, sensitivity signals reflecting changes in heat content exhibit a characteristic pattern in the three-dimensional continuum and have drastic temporal changes. This implies that the key regions will depend greatly on the operational timeframe of the observing system. We demonstrate a more effective geographic deployment strategy for the profiling floats monitoring changes in the oceanic heat content on a decadal timescale. At the beginning of the 2000s, great progress was made in ocean observations with the introduction of Argo profiling floats capable of continuously monitoring ocean properties  Figure . FollowiIt has been a contemporary interest of oceanographers to construct a practically effective ocean observing system within limited resources. Vecchi and Harrison  have invAlthough Vecchi and Harrison's approach can provide valuable information that leads to more effective ocean observing systems, the information was limited because it requires a set of independent model calculations based on some ad hoc scenarios. That is why the subsurface depth or sampling strategy is specified in their study. Their approach may therefore be rather favorable to sequential data assimilation, which requires relatively low computational cost.The adjoint solution of a general circulation model is known to enable us to detect the overall sensitivity of any objective function, for instance, water temperature in a specific location  or mass In this study, we report on adjoint sensitivity analysis using a four-dimensional variational (4D-VAR) ocean data synthesis system that was performed to identify the sensitivity of heat content in the entire Pacific Basin to a water temperature change for a multidecadal timescale. This variable  is always of central interest to oceanographers and climate researchers and is particularly relevant to global warming studies –7. We thA 4D-VAR ocean data synthesis system, developed as a part of the Japan Agency for Marine-Earth Science and Technology (JAMSTEC)-Kyoto University collaborative program (known as “the K7 consortium”) , 9 is apJ is here determined as the heat content integrated from 120°E to 70°W and from 60°S to 60°N over the entire Pacific Basin from surface to bottom. The adjoint model of an OGCM can be used to calculate the sensitivities, ∂J/∂X, where X is any variable of concern at location r and at time t. We are interested in determining how a shift in model variables would affect J. We therefore consider the form of δJ:δX is an estimate of the uncertainty . In this analysis experiment, ∂X was represented by a positive value whose magnitude is relevant to a change in subsurface water temperature by 1 Kelvin. This value does not imply any loss of generality. The change is assumed to be expressed as the delta function.Objective function J, in the same way as Masuda et al. [In this study, we made use of an optimized model climatology of the seasonal progression as the background ocean state for the determination of a et al. . The ocea et al.  and an oa et al. . We perfJ/∂X, where J is the integrated heat content over the entire Pacific Basin and X is water temperature. This corresponds to the possible change in water temperature taking place in the entire Pacific Basin at an allocated model time (defined as year zero) when water temperature changes at an arbitrary 3-dimensional grid point on the contour surface over a specific time period . For example, a contour surface of 0.9 at −10 years denotes that a given 1-degree change in water temperature in a specific volume on that surface would possibly cause a heat-content change that is relevant to temperature change by 0.9 degrees in the volume after 10 years. Thus, the value shows how influential the temperature change is in its contribution to the heat-content change after each time period.The values at shallow depths decrease as the retrospective time increases Figures . This isThe major distribution of the sensitivity is dominated by the circulation pattern within the first decade. During this stage, the advective effect stands out. Relatively large values are found in the recirculation regions of the horizontal large-scale circulation . The senWe investigated the role of wave motion at the specific depth of 1000 m, which was selected because of its strong relevance to the permanent thermocline in the midlatitude Pacific. The 1000 m isobath, in particular, is also a major drifting depth for Argo floats . The nonIn this section, we make best use of the adjoint sensitivity to define more effective deployment of the Argo profiling float. The sensitivities described in To evaluate the practical importance of each region for the detection of the heat-content change in the Pacific Basin, we have calculated the product of the sensitivity values  and the Over a 50-year period, values gradually diminish and the contrast changes region by region. For example, the rate of decay is relatively higher in the equatorial region, according to the temporal evolution of the sensitivity signal . These rTo demonstrate the effectiveness of a systematic deployment deduced from our analyses, we have performed a quantitative assessment for the case of a monitoring program aimed at specifying the decadal evolution of the heat content in the entire Pacific region. We chose two sets of 1652 grid points in a rectangular region of the Pacific Ocean, from 60°S to 60°N and from 120°E to 70°W. This value (1652) corresponds to the number of oceanic observation sites spaced at 3° of latitude by 3° of longitude across the region. The first of these two sets follows a conventional deployment pattern on a regularly assigned grid  [The total value of the observational sensitivity derived from the “optimal” observing system is 1.21 times that of the conventional one. This implies that intensive deployments in key regions can possibly enhance the accuracy of estimation for the heat-content change in the entire Pacific Basin by 20% for the same resource.The detailed values can depend on the model platform  and various assumptions made in an adjoint sensitivity analysis , 12. ForWe have conducted an adjoint sensitivity analysis with regard to changes in heat content in the Pacific Ocean using a 4D-VAR (adjoint) ocean data synthesis system. The results provide important insights into the factors influencing optimized designs of global observation schemes for enhanced ocean-state estimation on multidecadal timescales. In particular, this analysis enables us to provide useful information on effective geographical configurations for intensive deployment of Argo profiling float for the detection of the change in an important parameter associated with thermal changes in the ocean.The sensitivities show different patterns depending on the timescale required to perform the measurements in relation to the targeted climate variations or metrics. Our results suggest that the optimal observational configuration is a sensitive function of the targeted climate variations.Our 4D-VAR data synthesis system shows that a strategic geographical distribution of profiling floats deduced from the sensitivity analysis can potentially enhance the accuracy of estimation for a heat-content change by as much as 20% in a case.


This paper proposes the development of an advanced fuzzy logic controller which aims to perform intelligent automatic control of the yaw movement of wind turbines. The specific fuzzy controller takes into account both the wind velocity and the acceptable yaw error correlation in order to achieve maximum performance efficacy. In this way, the proposed yaw control system is remarkably adaptive to the existing conditions. In this way, the wind turbine is enabled to retain its power output close to its nominal value and at the same time preserve its yaw system from pointless movement. Thorough simulation tests evaluate the proposed system effectiveness. The joint consideration of both environmental concerns and economic issues has triggered an ever-increasing thoughtfulness on renewable energy resources. For instance, European Union aims to succeed by 2020 in decreasing greenhouse gas emissions by 20% (compared to 1990 ones), by increasing the amount of renewable energy to 20% and reducing the overall energy consumption by 20% through energy efficiency through the implementation of the 20/20/20 initiative [A great part of the scientific research on renewable energy resources focuses on wind power, that is, the conversion of the energy coming from flowing air into electricity which is performed through the utilization of air turbines –5. Wind However, despite the mostly promising prospects of wind energy, there are still many issues regarding the efficient harvesting of wind power which should be effectively handled. More specifically, both the velocity and the direction of wind are highly variable parameters thus making practically infeasible the total exploitation of the current wind momentum. Additionally, although low wind results just in low power output, high velocity wind may cause severe failure of many of the mechanical components of the wind turbine .These changes in the wind parameters may occur rapidly and in short time intervals. Consequently, the control of the wind turbine movement and reactions is needed to optimize its operation. Pitch and yaw control are the most common and effective ways that modern wind turbines utilize to increase power output .The rest of this work is organized as follows. In In a wind turbine, which has the ability to orientate its rotor towards the wind, the so-called yaw system is the component responsible for this operation.The simplest type of yaw control may be achieved through the use of the so-called passive yaw control systems which use the wind force so as to not only rotate the rotor but also orientate the wind turbine nacelle. The typical form of such systems consists of a roller bearing connecting the tower and the nacelle, along with a tail fin mounted on the nacelle which aims to apply an apt torque to the nacelle so as to turn the turbine rotor to the direction of wind. Passive yaw control offers a low cost solution which is effective mainly in small wind turbines.On the other hand, more advanced control capabilities may be provided through the use of the so-called active yaw systems which are applied to the majority of modern medium and large sized wind turbines. The main feature which differentiates them from passive yaw systems is that they include mechanisms able to produce torques in order to suitably revolve the nacelle of the wind turbine according to the current wind parameters.A typical active yaw system consists of a yaw bearing that provides the rotating joining between nacelle and tower, a yaw drive (yaw motor and gearbox), and the controller. In most cases, a yaw brake is also needed to provide a counter torque. Normally, wind direction signal originated from the wind sensor is the input to the controller. The yaw control system aligns the turbine's nacelle with the wind direction in order to minimize the yaw angle error, that is, the result of the subtraction between turbine main axis angle and wind direction.While the yaw angle misalignment correction lies in the center of the yaw control schemes –12, certThe control design depends on the choice of the motor (system actuator) due to the different operational characteristics of the types of motors. For instance, stepper motors are considered highly accurate actuators and in comparison to other DC or AC motors they do not need velocity control during their operation –15.Three-term (PID) or other conventional feedback controllers are applied in numerous control applications. In the cases, where there is a mathematical model in hand, such controllers are considered to be particularly accurate. However, their nature, which is highly linear and symmetrical, obstructs their successful utilization in nonlinear circumstances. Heating and the production of wind power are typical examples of this type of applications. When dealing with such applications, other types of control systems like fuzzy logic, fuzzy-PID controllers, neural networks, or a combination of them are more suitable because they can handle nonlinear models more effectively –22.Modern research works focus on the use of fuzzy logic in yaw control –27. SomeThe research work presented in this paper focuses on the yaw control of wind turbines through the development of a fuzzy controller which is designated to perform adaptive regulation of the orientation of the wind turbine rotor towards the wind in correspondence with the wind parameters that exist in the area surrounding the wind turbine. The enhancement provided by the proposed control system is that, contrary to other systems which perform fuzzy yaw control , the conThe simulation model adopted for the proposed yaw control system was built by using Matlab/Simulink environment. As shown in The stepper motor which is incorporated in the aforementioned model is supposed to have its basic construction similar to that illustrated in Generally, a typical permanent magnet stepper motor has the positioning accuracy advantage and a higher torque/volume ratio when compared to variable reluctance motors.Precisely, the rotor unit of the specific motor incorporated in the developed model utilizes the standard full step operation and rotates by 1.8° degrees per step.The motor driver utilizes signal modifying blocks. These blocks are utilized aiming at converting constant signals into properly synchronized pulses for the motor to operate with. In this way, considerable accuracy in positioning is achieved.The infrastructure of the stepper motor driver incorporated in the overall model is graphically presented in The wind farm module, which is integrated in the overall simulation model developed, includes a Double fed induction generator (DFIG) wind turbine , 28 whicThe main principle of a DFIG is that the windings of the rotor are connected to the grid by the use of slip rings and back-to-back voltage source converter which regulates not only the rotor but also the volumes of the grid currents. As a result, rotor frequency may be independent from the grid frequency. The DFIG technology allows extracting maximum energy from the wind for low wind speeds by optimizing the turbine speed, while minimizing mechanical stresses on the turbine during gusts of wind.During the simulation tests performed, the wind velocity was supposed to take values in the range from 6 m/sec (cut-in) to 30 m/sec (cut-off). Similarly, the nominal power per wind turbine reaches 1.5 MW.P of a wind turbine [ρ symbolizes the air density, R stands for the effective radius of the turbine, v represents the mean value of the wind velocity at the height of the rotor axis, Cp is the so-called power coefficient or else aerodynamic efficiency, λ represents the tip velocity ratio of the rotor blade tip velocity to wind velocity, β symbolizes the blade pitch angle, n is the electromechanical efficiency, and θ expresses the yaw misalignment angle. Consequently, the wind turbine inner blocks were appropriately designed in order to conform to what  and processes according to the analytical models described in , 23, 24.More specifically, the FIS adopted is based on the model proposed by Takagi-Sugeno , 30. TheThe use of this fuzzy modeling method offers two main advantages. The first of them is that it provides a simpler yet effective alternative approach to powerful conventional control theory for the analysis and control of complex nonlinear systems. The second advantage is that Takagi-Sugeno models utilize a radically smaller number of control rules than other fuzzy models . A synopThe fuzzy controller developed incorporates three inputs, which, are namely, error, error change, and wind velocity. The output of the controller is the input signal to the stepper motor's driver. The driver converts this constant signal into a series of appropriate pulses, in the form illustrated in The yaw error input signal is derived as the result of the subtraction of the wind direction angle minus the yaw motor angle. It is represented through the use of 7 membership functions. The range of angle values of each one of the membership functions corresponds to an acceptable yaw error angle for each of the three ranges of wind velocity which are described later on. The total range of angle values represented in this way is from −180° to 180°.Additionally, the change of error signal provides information on both the relative deviation of the yaw error around the reference point and the velocity of this deviation. In a similar way, with the yaw error, the change of error signal is also represented through the use of 7 membership functions.Furthermore, the current value of wind velocity is incorporated in the overall control model. This parameter is represented through the use of 3 membership functions which correspond to wind velocities in the ranges of 6–14 m/sec, 15–24 m/sec, and over 25 m/sec, respectively. The utilization of these input membership functions enables the full coverage of the total operational range of the wind turbine from the cut-in (6 m/sec) velocity to the cut-off (30 m/sec) velocity.The first set of simulations performed took place without the use of the fuzzy controller, in order to explore the behavior of the wind turbine for different yaw angle errors.The simulation scenarios examined refer to three different values of wind velocity, that is, 10 m/sec, 15 m/sec, and 25 m/sec (where the wind turbine is considered to operate properly).For each one of these values of wind velocity, the power output of the wind turbine was measured while the yaw error was consecutively set to be equal to 0°, 3°, 5°, 10°, 15°, 20°, 30°, 45°, 50°, 60°, and 89°.The results of the simulation tests which demonstrate the influence of the change of yaw error angle to the deviation wind turbine power output are summarized in The examination of the simulation data presented in Furthermore, it becomes apparent that for every wind velocity there is a threshold beyond which the increase of yaw angle error causes a practically perceptible reduction of power output and thus the additional operation of a controller unit is necessitated in order to confront this effect. The underlined data in v = 10 m/sec, although the rise of yaw error angle from 0° to 10° causes a relatively trivial reduction of power (by less than 4%), the further increase of yaw error angle by 10°, that is, from 10° to 20°, reduces power output down to 17.6% of the nominal value for this specific wind velocity. This can be graphically observed through More specifically, referring to the case where This behavior can be explained by taking into account the electrical and pitch angle control the wind farm module possesses; for example, when the power is high due to high wind speed and proper wind direction, the rotor speed is controlled by the pitch angle of the blades in order to smooth out power fluctuations.v = 15 m/sec, although the rise of yaw error angle from 0° to 30° reduces power by only 2.2%, the further increase of yaw error angle by 15°, that is, from 30° to 45°, decreases power output down to 48.9% of the nominal value for this specific wind velocity. This is depicted in Similarly, when v = 25 m/sec, this effect becomes even more evident because although the rise of yaw error angle from 0° to 45° decreases power by just 1.1%, the further increase of yaw error angle by 5°, that is, from 45° to 50°, results in a power output drop down to 40% of the nominal value for this particular wind velocity. This is noticeably illustrated in In the case where Therefore, based on these observations, it becomes profound that a yaw control regulator is necessitated, able to intervene adaptively to the existing values of wind velocity and yaw error angle.The performance of the fuzzy controller developed was initially tested through simulation tests over three different values of wind velocity  in order to check if the three levels of movement sensitivity are applied.Finally, the effectiveness of the proposed fuzzy yaw control system was investigated. This was achieved by setting up and conducting simulation tests in which the performance of the overall wind farm model was examined and validated under the same combinations of values of wind velocity and yaw error angle as the aforementioned.The corresponding simulation results are summarized in More precisely, these results indicate that the suggested fuzzy controller has successfully embedded three levels of yaw movement sensitivity.The first level of sensitivity corresponds to wind velocities below 15 m/sec and performs yaw rotations only for errors greater than 15° angle. This is graphically presented in Similarly, the second level of sensitivity refers to wind velocity ranging from 15 to 24 m/sec and yaw error being greater than 30°. This is illustrated in In the same way, the third level of sensitivity corresponds to the case where wind velocity is higher than 25 m/sec and yaw error is greater than 45°. This is depicted in It must be noted that the above plots begin with the nominal value of power output; that is, they refer to the steady state, because the imprint of simulation time before steady state is omitted.This is due to the fact that this time is excessively extensive due to the long time constants of the different electromechanical parts and the slow regulators of the model. Fluctuations of power output that exceed the nominal value during the simulation are regulated by the pitch and power control systems of the wind turbine model.It should also be noted that in order to change the acceptable yaw angle range or the wind velocity range for the levels of sensitivity, it is adequate to relocate properly the error input membership functions. The fuzzy rules are already tuned and do not need to be altered. Thus, the controller is easily adaptable to other models that operate in different environments.Higher movement sensitivity results in both higher power output and faster wear of the system. Consequently, it is a matter of balance between the movement sensitivity and power output that each application should decide on.In this research article, the wind turbine yaw control issue was investigated. An enhanced fuzzy controller has been designed to be able to regulate the yaw movement of wind turbines.This novel controller has the ability to take into consideration both the direction and the velocity of wind and to appropriately adjust with a variable sensibility to this momentum.This is the reason why the proposed wind turbine yaw control system achieves remarkable adaptation to the existing conditions.Simulation tests performed demonstrate the capability of the proposed system to retain the wind turbine power output close to its nominal value and at the same time prohibit any unnecessary movement of the yaw system.