It is important to consider and provide an account of this field-by-field variability. The field-specific ability beliefs (FAB) hypothesis aims to provide such an account, proposing that women are likely to be underrepresented in fields thought to require raw intellectual talent—a sort of talent that women are stereotyped to possess less of than men. In two studies, we provide evidence for the FAB hypothesis, demonstrating that the academic fields believed by laypeople to require brilliance are also the fields with lower female representation. We also found that the FABs of participants with college-level exposure to a field were more predictive of its female representation than those of participants without college exposure, presumably because the former beliefs mirror more closely those of the field’s practitioners (the direct “gatekeepers”). Moreover, the FABs of participants with college exposure to a field predicted the magnitude of the field’s gender gap above and beyond their beliefs about the level of mathematical and verbal skills required. Finally, we found that beliefs about the importance of brilliance to success in a field may predict its female representation in part by fostering the impression that the field demands solitary work and competition with others. These results suggest new solutions for enhancing diversity within STEM and across the academic spectrum.Women’s underrepresentation in science, technology, engineering, and mathematics (STEM) fields is a prominent concern in our society and many others. Closer inspection of this phenomenon reveals a more nuanced picture, however, with women achieving parity with men at the Ph.D. level in certain STEM fields, while also being underrepresented in some  Scientific American Mind begins: “Try this simple thought experiment. Name 10 female geniuses from any period of history. Odds are you ran out of names pretty quickly” : the more a field is believed to require raw brilliance, the fewer the women  sciences, technology, engineering, and mathematics (STEM). The general phenomenon is clear: on average, female representation in STEM fields (particularly those that are math-intensive) is lower than in the social sciences and humanities (SocSci/Hum). Though the magnitude of this gap has largely decreased across the last several decades, the difference is still reliable, prompting a number of efforts to explain it , STEM fields are characterized by female representation ranging from just under 20% (physics) to over 50% . We first asked participants to report on their beliefs regarding what was required for success in their own field, focusing on assessing beliefs about the relative importance of intrinsic, stable ability vs. effort and practice  to see women as somewhat unsuited for “brilliance-required” domains. Even in the absence of such biased treatment, widely shared ability beliefs similar to those previously identified in academics could lead young women to doubt that they could succeed in brilliance-focused disciplines and thus to decide against pursuing careers in them. Our main prediction is thus that laypeople’s beliefs, like those of academics, will predict female representation: the more a field is believed to require intellectual brilliance, the fewer the women.Results from We can also formulate a more detailed hypothesis here: people with more exposure to the fields in question  will have FABs that predict female representation more precisely than the beliefs of people with less exposure. We expect this to be the case because the FABs of those with more exposure to a discipline will likely be more similar to those of the practitioners of that discipline, and are thus more likely to be similar to the kinds of beliefs that students will encounter and absorb as they start to consider higher education and careers in these fields . In StudA final aim of Study 1 was to address an alternative explanation for the hypothesized relationship between ability beliefs and female representation. As we have argued, underlying the main predictions described above is our claim that FABs influence women’s academic and career choices. However, might laypeople’s beliefs be simply inferred from their pre-existing knowledge about the proportion of women in the different fields? For instance, our participants—particularly those who have had college experience in the relevant fields and thus have had the opportunity to witness gender disparities firsthand—might rely on stereotypes against women’s intellectual abilities to arrive at the conclusion that fields with few women must require high levels of such abilities, whereas fields with many women must not. To address this possibility, we asked participants to estimate the proportion of women in the fields under investigation, and assessed whether participants’ ability beliefs still predicted female representation independent from these estimates. If so, this would undermine the possibility that participants simply infer their ability beliefs from their estimates of the field’s diversity.beliefs about what is required for success in the fields under investigation. In particular, Study 2 examines two questions. First, do field-specific beliefs about the importance of intellectual brilliance reduce to beliefs about specific types of skills required for success? Specifically, do they reduce to beliefs about the degree to which mathematical and verbal skills are required for individual fields? Second, is the relationship between FABs and female representation mediated by beliefs about what kinds of work  are required?There are surely many other dimensions that vary among fields and influence the gender breakdown of the people who participate in them, and we do not claim that FAB is the only factor in determining academic gender gaps. Indeed, as we observed at the outset, other such factors have been evaluated extensively in prior studies  characterized by the most extreme gender disparities , it is unlikely that these beliefs are Finally, it is worth noting that, as in Study 1, college exposure may matter. Participants with college experience likely have more nuanced, differentiated beliefs both about which fields require mathematical skills and about which fields require intrinsic ability. We thus hypothesized that when looking specifically at individuals with college exposure, FABs would independently predict female representation over and above beliefs about math and verbal skills, supporting the idea that FAB can account for female representation across the academic spectrum.competition (vs. collaboration) and solitary work  that one can reveal how brightly one’s intellectual ability shines. Working with others in cooperative contexts, on the other hand, would make it hard to assess whose talent was responsible for any ultimate success attained, so this type of collaborative work may be assumed to be rare within fields that prize brilliance. The inference that brilliance-requiring fields involve solitary, and often competitive, work is also likely to be supported by pervasive cultural tropes that portray brilliance and genius as qualities that a person possesses and displays in isolation rather than as part of a team of collaborators  could be plausibly inferred based on the field’s presumed emphasis on brilliance, and that (2) men and women have diverging attitudes toward: namely, the extent to which the field requires rs e.g., . In turnestimates of female representation .Study 1 examined two main predictions, one broad and one more specific. Broadly speaking, we expected that there would be a relationship between laypeople’s FABs and female representation, such that fields believed to require brilliance would have fewer women. At a greater level of specificity, we expected that college exposure would differentiate the predictive power of FABs, such that the beliefs of those exposed to the fields during college would be particularly predictive. Finally, Study 1 also examined whether ability beliefs independently predicted female representation above and beyond people’s not reduce to people’s beliefs about mathematical skill, particularly when examining beliefs from individuals with college exposure in the field. Second, fields that are believed to require raw ability should also be perceived as requiring solo work and competition; in turn, these perceptions should predict gender gaps, with fewer women obtaining Ph.D.’s in fields assumed to demand high levels of solo work and competition. In other words, we expected that beliefs about solo work and competition would mediate  the observed association between FAB and gender breakdowns.Study 2 was designed to replicate the main findings of Study 1, and to extend the inquiry into additional beliefs that might relate to gender disparities. We made two predictions. First, we predicted that FABs would 2,3 . Only participants reporting themselves as living in the U.S. and with prior MTurk approval rates of 90% or above were included. Participants were compensated $0.75 for survey completion. Data were excluded from an additional 48 individuals who (1) failed to complete the survey, (2) answered an attention-check question incorrectly, (3) had IP addresses indicating they were outside the U.S., and/or (4) had IP addresses indicating they had completed similar studies in the past.Participants included 307 individuals recruited via Amazon’s Mechanical Turk (MTurk), an online crowd-sourcing platformn = 103; Version 2, n = 101; Version 3, n = 103). Each version included three humanities subjects, three social science subjects, and four STEM subjects. Each survey contained four questions assessing FABs about each of the 10 fields (from Table 2). Questions were presented individually in random order with all 10 fields listed beneath each question. Participants indicated their agreement with the statement as it applied to each field using a 7-point Likert scale . Two attention-check questions were also included to ensure that participants were attending to the task.To avoid participant fatigue, we created three versions of the survey, each of which contained 10 of the 30 fields under investigation. . Fieldslds from ; Table 2Next, a series of questions asked about participants’ academic exposure to the 10 fields, including whether they had had (1) a high school class, (2) a college class, and/or (3) a graduate-level class in each of them. Participants were also asked to estimate how many women had received American doctoral degrees in each field in the recent past, with 10 response options corresponding to 10% intervals ranging from 0 to 100%. A final set of questions asked about demographic information .4, (2) College Exposure FAB  and (3) No College Exposure FAB (using data from participants who had taken neither college nor graduate courses in the field). The four items had high internal reliability .For each field, we calculated FAB scores by averaging scores across participants from the four ability belief questions. Higher scores indicated more emphasis on brilliance. Three separate FAB scores were calculated: (1) All Participants’ FAB finer-grained level than those of people with no college experience. In particular, we expected that the College Exposure, but not the No College Exposure, FAB scores would predict female representation even after taking into account a gross STEM vs. non-STEM distinction between fields, which would speak to the ability of the College Exposure FAB scores to predict the complex field-by-field variability in female representation observed within these broad domains. Finally, we examined whether beliefs of college-exposed and non-college-exposed individuals predicted actual female representation independent of participants’ estimates of female representation. If so, this would rule out the possibility that ability beliefs predicted female representation for the trivial reason that they were inferred from participants’ pre-existing knowledge about gender disparities.Study 1 tested two main predictions. First, we expected that participants’ FABs would be correlated with female representation regardless of participants’ level of direct prior exposure with the fields (via courses). Second, we predicted that beliefs held by individuals with college experience would nevertheless be predictive of female representation at a r(27) = -0.59, p = 0.001 .To assess our first prediction, we examined the correlation between FABs and female representation. Any fields for which we received fewer than 10 participants in either the no-college-experience or college-experience samples were removed from the analysis; estimates based on so few participants would likely be unreliable. This resulted in 29 fields being retained for analysis.  As predicted, fields believed to require brilliance had lower female representation, r(27) = -0.67, p < 0.001, and No College Exposure scores, r(27) = -0.51, p = 0.005. Steiger’s z score comparison . Two separate multiple regression analyses were performed with female representation as the dependent variable and two predictors: a STEM/non-STEM indicator variable and either (1) College Exposure FAB scores or (2) No College Exposure FAB scores. These analyses indicated that, as hypothesized, the FABs held by participants with college exposure to the fields were uniquely predictive of female representation, above and beyond whether the fields were in STEM or SocSci/Hum , whereas the beliefs of participants without college exposure were not .To address the second prediction, we separately examined beliefs held by people with college exposure and those held by people without college exposure. Beliefs of both groups were significantly negatively associated with female representation: College Exposure scores, mparison  indicatep = 0.043; see Table 3). In contrast, the beliefs of participants without college exposure were not a significant predictor of female representation in this model . Thus, it is not the case that college-exposed participants’ ability beliefs are predictive of gender gaps across academia simply because they are derived from prior knowledge of such gaps.Finally, we added college-exposed and non-college-exposed participants’ estimates of female representation as predictors to the two regressions above. Consistent with our argument, the FABs of college-exposed participants remained a significant predictor of actual female representation even when adjusting for these participants’ estimates of female representation  were indeed higher than college-exposed women’s scores , t(28) = 4.02, p < 0.001, suggesting that men placed more emphasis on raw ability. In addition, our sample contained proportionately more college-exposed men in fields with lower female representation at the Ph.D. level, r(27) = -0.66, p < 0.001. To test whether these differences could explain our main result, we calculated a gender-balanced FAB score for each field by computing the average scores for men and women separately within fields, and then averaging these two gender-specific scores. This measure adjusts for the differential representation of college-exposed males and females across fields, giving the two groups an equal say in determining the FAB score for each field. If the current alternative explanation were correct, this gender-balanced score should no longer be predictive of female representation. However, when we entered the gender-balanced FAB score in place of the original FAB score in the regression including both STEM status and estimated female representation, it still predicted female representation . Thus, the main results described above were not merely a byproduct of men’s brilliance-oriented beliefs inflating the College Exposure FAB scores of fields with fewer women.We considered one final alternative interpretation, which applies particularly to the findings obtained with college-exposed individuals. Perhaps College Exposure FAB scores emphasize brilliance for fields where there are few women just because (1) men may be more likely than women to believe that brilliance is required for success, and (2) more men in the current sample may have taken college classes in disciplines where women are typically underrepresented. In other words, disciplines with lower female representation may have higher College Exposure FAB scores for the simple reason that male participants’ brilliance-focused ability beliefs are overrepresented in our sample for these disciplines. Consistent with this possibility, college-exposed men’s scores  failing to complete the survey, (2) answering an attention check question incorrectly, (3) having an IP address suggesting residence outside the U.S., and/or (4) having IP addresses indicating completion of similar studies (including our Study 1) in the past.n = 101; Version 2, n = 103; Version 3, n = 98). Surveys included the same four FAB items as in Study 1, along with two additional, broader questions on this topic (Table 2). These questions were added to further assess FABs, with the goal of using more accessible language while still providing a sensitive index of participants’ beliefs about innate ability vs. effort. Two items were also included to address people’s beliefs about the extent to which verbal and mathematical skills are required, and two final items were included to assess beliefs about whether competition and solitary work are important for success in a field (Table 2).As in Study 1, three versions of the survey were created, each of which contained the same subsets of 10 of the 30 fields under investigation. Approximately equal numbers of subjects participated in the three versions, and assignment was random . Two attention-check questions were also included. The survey then ended with questions assessing high school, college, and graduate level exposure to each of the 10 fields, along with several demographic questions. .We calculated FAB scores by averaging scores across the six items, and then averaging within fields to create field-level scores. Three separate FAB scores were calculated reflecting (1) All Participants’ FAB , (2) College Exposure FAB , and (3) No College Exposure FAB (using data from participants who had taken neither college nor graduate courses in the field). Scores for the six ability beliefs questions had high internal reliability . Deletion of the last two items added for Study 2 did not improve scale reliability, indicating it was appropriate to include them as part of the FAB scale.ns of 8, 4, and 3, respectively.) Replicating findings from Study 1, FAB scores were negatively associated with female representation when examining belief scores of all participants, r(25) = -0.63, p < 0.001, as well as when examining College Exposure scores, r(25) = -0.65, p < 0.001, and No College Exposure scores, r(25) = -0.54, p = 0.004. Although College Exposure scores were more strongly associated with female representation than No College Exposure scores, this difference was not significant according to Steiger’s z score comparison ; in contrast, the beliefs of those without college experience were not uniquely predictive when the STEM indicator was added . Thus, beliefs held by college-exposed individuals again predicted female representation better than those of non-college-exposed individuals.To explore whether Study 2 replicated the key finding that FABs predict female representation, we again examined correlations between FAB and percentage of female Ph.D. recipients. As before, fields with fewer than 10 participants reporting either college or no college exposure were removed. This resulted in 27 fields being retained for analysis.  = 0.63, p < 0.001; of participants with college exposure, r(25) = 0.63, p = 0.001; of participants with no college exposure, r(25) = 0.65, p < 0.001. Beliefs about the need for mathematical skills were negatively associated with female representation: beliefs of all participants, r(25) = -0.64, p < 0.001; of participants with college exposure, r(25) = -0.60, p = 0.001; of participants with no college exposure r(25) = -0.64, p < 0.001.We next examined the relationship between female representation and the extent to which a field is perceived as demanding verbal and mathematical skills. Beliefs about the need for verbal skills were positively associated with female representation: beliefs of all participants, with college experience (Table 4), FABs were uniquely predictive of women’s representation, above and beyond STEM status and beliefs about the importance of mathematical and verbal skill, β = -0.39, bootstrapped p = 0.085, although this coefficient was only significant at the α = 0.10 level. In contrast, beliefs about the importance of verbal and mathematical ability did not independently predict female representation in this model, ps > 0.489. For the regression testing the beliefs of those without college experience, no factor was significantly predictive of female representation, ps > 0.454 (Table 4).We then tested our prediction that FABs of individuals with college exposure would predict female representation independently from beliefs about the role of mathematical and verbal skills. If so, this would strengthen the claim that FABs tap into something distinct from people’s beliefs about which fields require mathematical aptitude. To assess this prediction, we added perceptions of the need for verbal and mathematical skill as variables in the two regressions predicting female representation. For the regression testing beliefs of those r(25) = -0.41, p = 0.03, indicating that college-exposed male participants were more numerous in fields with lower female representation. In this sample, however, college-exposed men’s FAB scores  were actually lower than college-exposed women’s scores , though not significantly so, t(26) = 1.69, p = 0.103. Thus, this alternative explanation is unlikely: college-exposed male participants, though more numerous in fields with fewer women at the Ph.D. level, did not differ from college-exposed female participants in their ability beliefs. Nevertheless, we entered a gender-balanced FAB score in place of the original FAB score in the regression model that also included a STEM indicator, beliefs about mathematical ability, and beliefs about verbal ability. As before, ability beliefs were the sole predictor of female representation . These results strengthen the main claim that ability beliefs are predictive of female representation, above and beyond beliefs about mathematical and verbal skills.As in Study 1, we also calculated a gender-balanced FAB score to examine the possibility that differences in male and female participants’ ability beliefs and college experience were driving the effects observed for college-exposed participants.  Again, the proportion of college-exposed male participants within each field was negatively related to female representation at the Ph.D. level, 5.  Results are thus consistent with the idea that FABs may influence women’s participation in a field in part by influencing their beliefs about what it is like to be a member of that field—in particular, whether one works by oneself or with others, and whether success rests more on competition with colleagues rather than cooperation. Interestingly, this result was observed even within the group who had not had college exposure to the field, which may be because inferences about the nature of the work demanded by various fields are easily drawn from one’s ability beliefs about these fields, no matter how much first-hand experience one has with them.Finally, we tested the prediction that beliefs about solo work and competitiveness would mediate the relationship between FABs and female representation. Consistent with our argument, a bootstrapped  product-of-coefficients mediation analysis performed with the PROCESS procedure in SPSS 22  revealedWomen are underrepresented in many STEM fields, but the pattern of gender distribution is complex, and a substantial amount of variation also exists in non-STEM fields. An important aim of the current studies was to provide an account for the wide variability in female representation across the entire academic spectrum. We maintain that the FAB hypothesis provides such an account. This hypothesis predicts that women will be underrepresented in fields believed to emphasize brilliance and inherent ability as the key to success; this is because women are often stereotyped as lacking the same sort of innate intelligence as men, and thus women will be discouraged from participating in fields to the extent that these fields are perceived as requiring this type of intelligence. Prior research has provided support for the FAB hypothesis within higher academia . The curSeveral additional findings from the present studies are worth highlighting. The ability beliefs of individuals who had college-level exposure to the fields in question predicted female representation even when controlling for whether a field was in STEM or not, indicating that college may provide a unique context for refinement and elaboration of beliefs about what fields require for success. Results also suggested that the ability beliefs of participants with college experience are not simply a byproduct of participants’ inferring these beliefs based on their prior knowledge of female representation (Study 1). Further, college-exposed participants’ ability beliefs capture something beyond perceptions of specific types of skills required for success, as FABs of college-exposed individuals did not reduce to beliefs about which fields require mathematical and/or verbal skills (Study 2). has achieved rather than on the person’s inherent traits (Notably, these findings have important consequences for potential interventions to improve diversity, both in terms of timing and in terms of content. College may be a pivotal experience during which people’s FABs become entrenched, and start to conform to those of their instructors. This highlights the crucial role that college educators play in communicating these maladaptive beliefs—but also suggests that they may be able to play an active role in changing the relevant messages. In particular, our data suggest that instructors who want to promote diversity might aim to minimize discussion of innate talent, regardless of the domain of skills with which it is associated, and instead highlight the importance of effort, practice, and persistence to success in a field. Prior work on individuals’ achievement beliefs suggests that such growth-oriented messages can be relayed in a range of ways: by choice of adjectives (in particular by avoiding words like “brilliant,” “genius,” etc.; , t traits , and by t traits . We expet traits . This int traits .The current studies also suggest that beliefs about solo and competitive work may mediate the relationship between ability beliefs and female representation. It is possible that this result reflects a process by which ability beliefs influence perceptions of what it is like to work in certain fields, which in turn may influence the participation of women in these fields. Of course, we acknowledge this is not the only possible pathway here; our mediation analyses were designed to test an a priori hypothesis regarding how ability beliefs relate to representation, but they cannot determine directionality. Similarly, causality regarding ability beliefs and female representation cannot be claimed from the current studies due to the correlational nature of the data. However, our theoretical model posits that ability beliefs do drive women’s career and educational choices, and recent experimental manipulations in our lab have provided evidence consistent with this causal claim e.g., . For insFurther investigating the precise pathways by which non-academics’ ability beliefs influence participation is one important topic for future research. To begin, it is worth noting that young men and women often decide whether or not to pursue a field long before interacting with professors, graduate students, or any other active practitioners of that field e.g., . Indeed,In summary, we have provided support for the FAB hypothesis, demonstrating that women tend to be underrepresented in fields believed to require innate intellectual talent for success. Our data also open up possibilities for future research on the pathways by which ability beliefs influence women’s participation. Finally, these studies point to possibilities for effective interventions. If the practitioners of fields with gender gaps made a concerted effort to highlight the role of sustained, long-term effort in achievement, the gender gaps in these fields may correspondingly be diminished.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.


Auxetic mechanical metamaterials are engineered systems that exhibit the unusual macroscopic property of a negative Poisson's ratio due to sub-unit structure rather than chemical composition. Although their unique behaviour makes them superior to conventional materials in many practical applications, they are limited in availability. Here, we propose a new class of hierarchical auxetics based on the rotating rigid units mechanism. These systems retain the enhanced properties from having a negative Poisson's ratio with the added benefits of being a hierarchical system. Using simulations on typical hierarchical multi-level rotating squares, we show that, through design, one can control the extent of auxeticity, degree of aperture and size of the different pores in the system. This makes the system more versatile than similar non-hierarchical ones, making them promising candidates for industrial and biomedical applications, such as stents and skin grafts. Hierarchical materials and structures are a class of systems which are composed of structural elements which themselves have structure1An equally interesting class of materials and structures are those designed to exhibit auxetic behaviour, i.e. exhibit a negative Poisson's ratio, which means they get wider rather than thinner when uniaxially stretched9101112Despite the advantages of auxetic and hierarchical materials, the concept of an auxetic hierarchical system has been poorly studied171820222325In this study, we propose and discuss a number of hierarchical auxetics based on rotating rigid units , were assigned stiffnesses of ϕ1) were given stiffnesses of ϕ1, which is related to θ1, the angle between through ϕ = θ1 + θ0. Three different cases were considered here, namely: Case I, where the ϕ1-hinges were set to be much stiffer than the θ0-hinges; Case II, where the stiffnesses were set to the exact opposite of those in Case I, and finally Case III, where all the θ0- and ϕ1-hinges were given low stiffness constants, i.e. both hinges were soft.To illustrate some of the properties and versatility of the proposed hierarchical structures, simulations were performed on the simple two-level system illustrated in νyz and νzy obtained from these systems are shown in θ0- and ϕ1- hinges. The change in angles that occur upon the application of on-axis uniaxial stress help us understand the deformations taking place upon loading . It was observed that the level 1 deformations associated with the ϕ1-hinges were much more significant than those of the θ0-hinges at level 0 , as planar ball and spring systems described by a harmonic potential as discussed in Grima y and z-directions.In all three cases, the squares were kept as rigid as possible by using the highest values for the stiffness constants to define the internal 90° intra-square angles and side lengths. Full details of the simulations are provided within the The concept of hierarchical rotating systems was developed by J.N.G. The simulations were performed by L.M., J.I.A. and K.M.A. J.N.G., R.G. and D.A. wrote the main manuscript text while the figures were prepared by L.M. and K.M.A. A.C. and J.B. contributed to the discussion of the manuscript mainly on the medical aspects of the work involved. The work was supervised by J.N.G. and R.G. All authors reviewed the manuscript before submission.ANIM01.gifSupplementary Information


The space immediately surrounding us is known to be represented relative to our hands, i.e. in a hand-centred coordinate system  . IndividHere, we examined the representation of peri-(missing)-hand space (P[M]HS) in one-handers, by interrogating their PHS network using functional neuroimaging. The PHS network is comprised of several brain regions, most prominently: the anterior and posterior parts of the intraparietal sulcus (IPS), the lateral occipital cortex (LOC), the supramarginal gyrus and the pre-motor cortex . A subseIf the PHS network is specifically anchored to the hand, then the absence of a hand should result in diminished P[M]HS representation (and possibly enhanced representation in relation to the intact hand). Moreover, areas known to selectively respond to visual features of the hand  should not be activated when objects are approaching the missing hand. If, however, PHS network is defined by the zone for object manipulation , represen = 9) for control purposes. Within each functional run a 3D moving object appeared in one of two locations: either near or far from the participants' body, as used in previous studies . A group comparison for near > far contrast in the handless-arm condition revealed increased activity in a subset of PHS network in one handers, relative to acquired amputees (see We next determined how one-handers' P[M]HS representation compares with another population with a hand-loss. We therefore compared P[M]HS in one-handers and in acquired amputees undergoing the same experimental procedure . While otees see . This suOur main finding shows that the P[M]HS evoked activity is present in one-handers despite congenital hand-loss. We suggest that PHS network, normally representing the space surrounding the hand, can adapt to represent the space surrounding the handless-arm in the absence of a hand. This reanchoring of PHS in one handers, and the finding of greater P[M]HS activity in one handers compared to amputees, can be interpreted differently under two existing frameworks. First, considering the evidence for PHS as an interface for effector-centred representation, and the suggested remapping of PHS during prosthesis  and tool


Intelligent video surveillance systems detect pre-configured surveillance events through background modeling, foreground and object extraction, object tracking, and event detection. Shadow regions inside video frames sometimes appear as foreground objects, interfere with ensuing processes, and finally degrade the event detection performance of the systems. Conventional studies have mostly used intensity, color, texture, and geometric information to perform shadow detection in daytime video, but these methods lack the capability of removing shadows in nighttime video. In this paper, a novel shadow detection algorithm for nighttime video is proposed; this algorithm partitions each foreground object based on the object’s vertical histogram and screens out shadow objects by validating their orientations heading toward regions of light sources. From the experimental results, it can be seen that the proposed algorithm shows more than 93.8% shadow removal and 89.9% object extraction rates for nighttime video sequences, and the algorithm outperforms conventional shadow removal algorithms designed for daytime videos. Recently, video analytics has been widely deployed in various application areas including video surveillance, business intelligence, and the Internet of Things ,3,4,5,6.Intelligent video analytics algorithms can be deployed in IP cameras or video analytics servers located in monitoring centers or cloud networks. A conventional video analytics algorithm based on background subtraction is shown in The performance of the event detection system mostly depends on the accuracy of foreground extraction, which is degraded by either foreground pixels absorbed into the background or shadow pixels detected as foreground. If the signal characteristics of foreground pixels are similar with those of the background pixels of the same positions, these foreground pixels can be considered as background. Also, it is highly probable that each shadow region will be extracted as foreground after background subtraction because the foreground intensity may be different from that of the background for the same position depending on the intensities of the illuminating light sources. Shadow regions are generally assumed to become darker than background regions, but they generally have similar characteristics in terms of chromaticity and texture with the background regions of the same position. Conventional shadow detection algorithms have used the similarities in color ,12,13,14Chromaticity-based shadow detection algorithms assume that background regions under shadow become darker but maintain their chromaticity; i.e., they exhibit color constancy. These algorithms choose color models of separate intensity and color components, such as normalized RGB , c1c2c3 Geometry-based shadow detection algorithms utilize the orientation and shape of the shadow regions, along with a knowledge of light sources, background surface condition, and object shapes such as those of vehicles ,16 and pTexture-based shadow detection algorithms utilize the fact that shadow regions keep most of their texture; using texture correlation, these algorithms compare the texture in the candidate shadow regions with that in the background. Various forms of texture correlation are proposed for shadow detection: gradient or edge correlation ,20, orthPhysics-based shadow detection algorithms use physics-based attenuation and color features to learn local or global shadow models ,27,28,29Due to the weakened signal strength of color and texture and increased noise power, these conventional algorithms have limitations in using color and texture features for shadow removal in nighttime video sequences. The conventional algorithms using the geometric characteristics of shadow ,18,22 arMachine learning based shadow detection algorithms have proposed frameworks that automatically learns the most relevant features of shadow in a supervised manner using multiple convolutional deep neural networks ,25,26. TIn nighttime video sequences, as in the example shown in The orientations of shadow regions can be argued to be strong features for shadow removal in nighttime video sequences. In this section, a novel shadow detection algorithm is proposed for nighttime video sequences; this algorithm uses the orientations of shadow regions toward the regions of light sources (RLS).For shadow removal in nighttime video sequences, four assumptions are made concerning the shapes and orientations of objects and shadow regions. First, each target object and its shadow region can be matched to ellipses with high aspect ratio. Second, the orientation of each shadow region, the direction of the major axis of the ellipse matched to the shadow region, heads toward a region of a light source existing inside or outside the video frame. Third, the horizontal axis of the video frame is parallel to the ground plane, and the orientation of each target object is perpendicular to the ground plane. Finally, the orientation of each target object is different from that of its shadow. When a target object is located between a light source and a camera, the orientations of the target object and its shadow are in similar directions. Because cameras are usually installed in locations that avoid counter-light, the case of similar orientations is excluded in this study.Under these assumptions, each foreground object is partitioned based on its vertical histogram, and the matched ellipses of the partitioned objects are calculated. The orientation of each matched ellipse is used to validate each partitioned object as a shadow region. If the orientation heads toward the pre-configured regions of light sources, the corresponding partitioned object is classified as shadow and removed from the foreground region it belongs to. The video analytics system with the proposed shadow detection algorithm for nighttime video sequences is illustrated in After background generation from the input video frames, binary foreground regions are extracted by background subtraction followed by median filtering for noise suppression. The proposed shadow detection algorithm is applied to the labeled foreground regions to provide final labeled object regions without shadow to the ensuing processes in the video analytics system. The proposed algorithm consists of histogram analysis, foreground partitioning, orientation calculation, and shadow decision and removal. By detecting abrupt changes in the vertical histogram inside each extracted foreground region, the foreground region is partitioned into one or multiple partitioned objects. For the calculation of the orientation of each partitioned object, that object is matched to an ellipse and the direction of the major axis of the matched ellipse, i.e., its orientation, is found. For each partitioned object, if its orientation heads toward the regions of light sources, it is classified as shadow and is used to make a shadow removal mask. Final object regions are obtained by masking the partitioned objects classified as shadow from the foreground regions.In nighttime video sequences, if the direction of a certain light is not similar to the orientation of a certain object, the object and its shadow appear as a merged foreground region that cannot be matched with a single ellipse, as shown in kth merged foreground region is represented in matrix form by its elements The bounding box jth column in the bounding box The vertical histogram of the K columns away from the current column is compared with that of the current column, the reference column, to aggregate enough of a histogram difference for partitioning. For histogram comparison, the number of columns that separate these two columns, K, depends on the resolution of the video frame; this number is 5 columns for D1 resolution in this study. If there exists a column for which the vertical histogram is larger or smaller than that of the reference column by the amount of a certain threshold, the reference column is determined to be a partitioning column. A zero column vector is overwritten to the partitioning column to delineate one partitioned region from the other in the region After calculating the vertical histogram, the histogram difference between adjacent columns is compared with a given threshold to partition the foreground region Shadow may exist either to the left or to the right of a foreground object, as shown in jth column vectors in For the calculation of a partitioned bounding box from an input bounding box, a foreground partitioning algorithm in a bounding box is proposed and is described in Algorithm 1. In the algorithm description, Algorithm 1: PartitionBBox (In this study, every foreground object is assumed to be in the form of an ellipse and to have a matched virtual ellipse. The orientation of a partitioned object is defined as the direction of the major axis of the matched ellipse of the partitioned object. The center of the matched ellipse is defined as the centroid of the partitioned object. The direction can be found by rotating the partitioned object clockwise with the rotation axis at the centroid until the difference between the maximum and the minimum y-coordinates of the pixels in the rotated partitioned object is minimized.x- and y- coordinates of the kth partitioned object, respectively.The centroid of a partitioned object can be determined as follows.θ in a clockwise direction. The angle between the major axis of the partitioned object and the horizontal axis, illustrated in If the lower left corner of a video frame is set to the origin, the major axis can be represented by the following line equation.Shadow regions in nighttime video sequences are formed by artificial light sources; their sizes and orientations are determined by their displacements from light sources. To estimate the orientation of each shadow, the locations of light sources should be known. Light sources in nighttime video sequences generally are not point sources, but ambient sources from buildings or explicit areas inside or outside the video frame, as shown in Although light sources may exist inside the video frame, regions of light sources are configured on the left region In the proposed shadow detection algorithm, if the major axis of a partitioned object passes through the RLS, this partitioned object is considered to be a shadow. If light sources exist in the region x-range of the RLS. The value of 1 represents a shadow region; 0 represents a foreground object.For each partitioned object, if object orientation heads toward the RLS, it is classified as shadow. The shadow indicator for each partitioned object is given as follows.The shadow indicator is used to make a shadow mask for a video frame; final foreground objects are obtained by masking the shadow regions from the input foreground regions.To evaluate the performance of the proposed algorithm, the video content analytics algorithm with the proposed method of shadow detection, shown in The proposed shadow detection algorithm is fed with the foreground regions and their bounding boxes, obtained using the foreground extraction module in the video content analytics algorithm. The performance of the proposed algorithm in terms of both pixel and object levels is compared with those of conventional algorithms that adopt different features for shadow detection in daytime.single is a video sequence with a single foreground object in every video frame in which there is no interference from other foreground objects or their shadow regions. The interference multiple is a video sequence with multiple foreground objects in most of the video frames in which there exists interference from neighboring foreground objects or their shadow regions. Although the proposed algorithm attempts to detect and remove shadow regions in nighttime video sequences, the performance for two daytime video sequences is measured for performance reference.To evaluate the performance of the proposed shadow detection algorithm, six nighttime and two daytime surveillance video sequences, listed in RLS in For each video sequence, RLS are configured outside the video frames based on the locations of light sources generating shadow. Although each partitioned object can be matched to an ellipse, the orientation of the matched ellipse may be inaccurate due to imperfect extraction of foreground regions. Also, the ground where foreground objects exist may incline to one side, which modulates the orientation of each matched ellipse with the grade of the slope. Although estimation errors in the orientations of matched ellipses are hard to predict for these cases, the errors are not so large as to considerably change the orientations. Therefore, only the existence of left or right light sources is considered for shadow removal; this is done simply by configuring entire left or right regions, For performance evaluation, the ground truths are generated by painting foreground objects by hand; these objects are compared with the final foreground objects generated by the proposed shadow detection algorithm. Because the proposed algorithm is fed by the foreground regions from the foreground extraction module, consisting of background subtraction and thresholding, only the extracted region of each foreground is considered as the ground truth. Foreground regions not extracted because their statistical characteristics are similar to those of the background are not included in the ground truth.Two performance measures for shadow detection and the ensuing process in the video analytics system are defined: shadow removal rate and object extraction rate. Shadow removal rate is defined as the measure of the performance of shadow removal from the extracted foreground regions at the pixel level, as follows.For shadow detection in video content analytics systems, it is important to measure how shadow removal affects the performance of object extraction. In the i-LIDS guide , the corFor a single object, there is no possibility for each shadow region to interfere with other objects. However, to prevent false alarms in event detection, shadow removal for a single object is also required for video content analytics because a shadow region is sometimes separated from its host object and detected as a new object; or, it intrudes on regions of interest while its host does not.Although the final foreground objects after shadow removal still include several shadow pixels, as can be seen in the red enclosed regions in For multiple objects, some objects are sometimes interfered with by shadow regions of other objects if the objects are close enough to be connected by shadow regions. The proposed algorithm can also remove shadow regions between neighboring objects by partitioning foreground regions based on vertical histogram comparison and validation of the orientations of partitioned objects. Three objects in Fragmented or incomplete foreground regions due to imperfect foreground extraction in the video analytics system may be detected as shadow regions if their orientations accidentally head toward the RLS. These problems of small shadow regions merged with foreground objects and the removal of incompletely extracted foreground regions can be resolved by applying features used in daytime shadow removal such as color and texture or by using object tracking information; these subjects are not considered in this study and are left for further study.Using the shadow removal rate in Equation  and objeThe proposed algorithm shows a 93.8% shadow removal rate and a more than 40.0% enhancement over BSR in average object extraction rate for nighttime video. The object extraction rate of the proposed algorithm for sequence S4 cannot be acceptable for video analytics. The performance enhancement for sequence S4 is limited because the objects in the scene are quite close to each other, close enough to disturb the object extraction process; the front fence sometimes separates a single object into several smaller blobs, and some objects in the video frames of sequence S4 are less illuminated by light sources.For daytime video sequences, all the algorithms showed better shadow removal rates than they did for nighttime video. Especially, the physics based algorithm and the proposed algorithm are superior to the others in object extraction rate.For accurate object tracking, merge and separation of multiple objects should be handled appropriately. Shadow regions between neighboring objects may cause merging of neighboring objects and result in the loss of object information. If multiple objects are connected by shadow, these objects are usually labeled as a single object, losing their object information.The shadow removal performance for multiple objects connected by shadow is evaluated for the proposed algorithm. Among the multiple object sequences in It can be shown that the proposed algorithm, by removing shadow between neighboring objects, can prevent performance degradation due to object merger by shadow in normal nighttime video surveillance sequences. Although the proposed algorithm has a limitation in removing shadow pixels underneath objects, this limitation does not cause object merging or performance degradation in object tracking. However, for complex nighttime video sequences, further study to consider texture and color components together with the orientation of the partitioned object will be required to prevent performance degradation.In this paper, a novel shadow detection algorithm is proposed for object extraction in nighttime video sequences; this algorithm validates the possible orientations of shadow toward the region of light sources. Each extracted foreground region is partitioned by double scan based vertical histogram change detection, each partitioned object is matched to an ellipse, and the orientation of the matched ellipse is used for the validation of the partitioned object as shadow. The proposed algorithm is shown to quite accurately remove shadow in nighttime video sequences with a single object or multiple objects, with a 93.8% shadow removal rate; this algorithm improves the object extraction performance by suppressing the interference among neighboring objects caused by their shadow regions.The proposed shadow detection algorithm, combined with a conventional daytime shadow detection algorithm, can be used around the clock in intelligent video surveillance systems to detect pre-configured surveillance events based on object extraction.The proposed algorithm has a limitation in handling small partitioned objects, such as small shadow regions between objects and incomplete foreground regions, of which the orientations are not explicitly discernible. This limitation can be resolved by applying features used in daytime shadow removal such as color and texture or by using object tracking information. The comparative study with machine-learning approach is also required for various video surveillance environments. These topics will be left for further study.


Young women frequently drink alcohol in groups and binge drinking within these natural drinking groups is common. This study describes the design of a theoretically and empirically based group intervention to reduce binge drinking among young women. It also evaluates their engagement with the intervention and the acceptability of the study methods.Friendship groups of women aged 18–35 years, who had two or more episodes of binge drinking  in the previous 30 days, were recruited from the community. A face-to-face group intervention, based on the Health Action Process Approach, was delivered over three sessions. Components of the intervention were woven around fun activities, such as making alcohol free cocktails. Women were followed up four months after the intervention was delivered.The target of 24 groups (comprising 97 women) was recruited. The common pattern of drinking was infrequent, heavy drinking (mean consumption on the heaviest drinking day was UK 18.1 units). Process evaluation revealed that the intervention was delivered with high fidelity and acceptability of the study methods was high. The women engaged positively with intervention components and made group decisions about cutting down. Twenty two groups set goals to reduce their drinking, and these were translated into action plans. Retention of individuals at follow up was 87%.This study successfully recruited groups of young women whose patterns of drinking place them at high risk of acute harm. This novel approach to delivering an alcohol intervention has potential to reduce binge drinking among young women. The high levels of engagement with key steps in the behavior change process suggests that the group intervention should be tested in a full randomised controlled trial. Binge drinking among young women is a recognised public health problem . Binge dReducing the alcohol consumed during binge drinking sessions is challenging as heavy drinking is viewed by many as a normal activity and being extremely drunk is socially acceptable . DrinkinAlcohol brief interventions (ABIs) are widely used to tackle problem drinking . ABIs arReducing harmful drinking by young women is complex, because interventions have the potential to challenge relationships that are highly valued. Group norms can encourage heavy drinking , 30, butThis study describes the design and assesses the acceptability of a community based, tailored intervention with pre-existing friendship groups to tackle binge drinking among young women. The novel intervention addresses drinking as a fundamental part of friendship, and seeks to highlight how fun and friendships can be maintained while reducing binge drinking. The objectives for the study were to develop and test the feasibility and acceptability all of the methods that will be required for a full randomised controlled trial. Feasibility will be measured by the success of recruitment, retention, measurement of outcomes, delivery of the intervention and engagement with the intervention. Acceptability will be assessed by a post-study evaluation of participants’ experiences of the study. The UK MRC guidelines on developing and evaluating complex interventions  stress tEthical approval for the study was obtained from the University of Dundee Research Ethics Committee (Reference: UREC 12072). Women, aged 18–35 years, who regularly socialise and drink together, were invited to take part in the study with their friendship groups. For the study ‘friendship group’ was self-defined by the participants as a group who regularly drank together. The age range was chosen because women in this group have the highest prevalence of binge drinking among women in the UK ‘‘I thought it was a good idea to help out for the study and also to think about how excessively we drink sometimes’The majority of women gave positive responses to questions assessing the acceptability of study. Almost 70% of the participants (57 women) who were followed up reported that they had discussed the study with others , while 76 (90%) said they would recommend the study to other women.In response to a question on the perceived benefits of taking part in the study, 71 participants (85%) said they benefitted and gave reasons why. Thirty five women reported that the study had raised awareness about their alcohol consumption:‘The sessions made me more aware of not only my own but my peers  drinking habits. When we discussed what was involved before a night out in the “getting ready” process I was unaware of how much my friends and I actually drank before actually heading out’.Another perceived benefit (for 13 women) was that they were more likely to reflect on their drinking after taking part in the study:‘I feel that I have realised that limiting what I drink can be beneficial to how I feel about myself. If I don’t drink then I don’t have a horrendous hangover and that I feel I have more control’Setting group goals and action plans were key components of the behavior change strategy. Sixteen women reported that this session had been particularly useful:‘Hadn’t heard of SMART goals before. Easy to set big goals but hard to achieve. More appropriate to make small steps’.Women were asked whether they had learned any useful techniques during the study. Many related tips on how to avoid becoming very drunk such as:‘Saying no. Finding other ways to socialise and have fun. Thinking healthy. Taking more pride in myself.’‘I’ve realised that it’s important to reward yourself for setting goals and achieving them, and doing something different like a mocktail class with friends can be really good fun’The role of the friendship group was emphasised in the study evaluation. Women realised, that at the beginning of the study, they were not aware of what group members felt about drinking, and were unclear about their group’s motivation for drinking:‘Interesting to hear everyone’s thoughts on drinking as it is not something that is usually discussed’‘Being honest about our drinking habits and how it impacts on our lives’Some women reported gaining confidence in being able to refuse drinks when they were with the group:‘Being able to talk to my friends when I don’t want to drink and them accepting I’m monitoring how much I drink’The support of the group was important, particularly in implementing goals and action plans:‘Being part of a group aiming for the same goal makes it more attainable’NOT to do shots now which I never thought would happen’‘Definitely follow the goal we set. A lot easier to do when everyone you are out with has the same goal. A bit of peer pressure The perception of having fun endured to the end of the study, but many participants also reported that the experience had been useful and interesting, and in some cases, brought the group closer together:‘I think combining the sessions with fun activities was definitely important as it encouraged us to find new ways of spending time together rather than drinking’‘Benefited our friendship, discussed new activities to do together’This study has demonstrated that friendship groups of young women who engage in heavy binge drinking can be recruited to an alcohol intervention study. The use of a novel method of delivery, fun activities that provide a platform for behavior change activities, may have encouraged participation. The intervention was successfully delivered with almost all groups of women setting group goals and making action plans to reduce their drinking. Process evaluation indicated high levels of engagement with components of the behavior change strategy and retention was high. The post study evaluation showed high acceptability of study methods, and highlighted the important role of the friendship group in reducing hazardous drinking.This is the first study to report recruiting and intervening on natural drinking groups in an alcohol intervention. Alcohol interventions have been delivered to groups of female students, but these did not involve natural drinking groups , 62. ParA strength of the study was the ability to monitor engagement with components of the behavior change strategy in real-time. The flip charts were used as part of the intervention delivery to record the pros and cons of being drunk, the benefits of moderated drinking, goal setting, action and coping planning, and maintenance strategies. These also provide unobtrusively collected real-time data on the participants’ responses to the intervention components. They demonstrated that the women successfully carried out key tasks in the behavior change process (e.g. implementation intentions  and moniA high follow-up rate (87%) was achieved, which is higher than many alcohol brief intervention trials . It was A possible weakness of this study is that the time period over which the intervention was delivered. Study sessions were held approximately one week apart. Some groups reported that they had insufficient time to implement their plans to reduce binge drinking before returning for the third session. For the full trial the intervention should be held over a longer period, four to six weeks, with a longer period between session 2  and session 3 (behavior maintenance).This feasibility study did not have a comparator group. Its purpose was to determine whether women could be recruited and retained in a novel group intervention study on alcohol, whether they would engage with the intervention and find the study methods acceptable, and whether the proposed outcome measures could be measured , 66. AltThis study has shown that targeting natural drinking groups of young women provides a unique opportunity to reduce binge drinking. The use of the fun-based activities aided recruitment and promoted engagement with the intervention. The intervention successfully prompted the young women to set goals and make action plans. This approach has great potential, particularly for groups who are unaware that they are drinking at hazardous levels. This intervention should be tested in a full randomised controlled trial.S1 Table(DOCX)Click here for additional data file.S2 Table(DOCX)Click here for additional data file.S3 Table(SAV)Click here for additional data file.


Saturation has attained widespread acceptance as a methodological principle in qualitative research. It is commonly taken to indicate that, on the basis of the data that have been collected or analysed hitherto, further data collection and/or analysis are unnecessary. However, there appears to be uncertainty as to how saturation should be conceptualized, and inconsistencies in its use. In this paper, we look to clarify the nature, purposes and uses of saturation, and in doing so add to theoretical debate on the role of saturation across different methodologies. We identify four distinct approaches to saturation, which differ in terms of the extent to which an inductive or a deductive logic is adopted, and the relative emphasis on data collection, data analysis, and theorizing. We explore the purposes saturation might serve in relation to these different approaches, and the implications for how and when saturation will be sought. In examining these issues, we highlight the uncertain logic underlying saturation—as essentially a predictive statement about the unobserved based on the observed, a judgement that, we argue, results in equivocation, and may in part explain the confusion surrounding its use. We conclude that saturation should be operationalized in a way that is consistent with the research question(s), and the theoretical position and analytic framework adopted, but also that there should be some limit to its scope, so as not to risk saturation losing its coherence and potency if its conceptualization and uses are stretched too widely. In broad terms, saturation is used in qualitative research as a criterion for discontinuing data collection and/or analysis.‘What?’—in what way(s) is saturation defined?‘Where and why?’—in what types of qualitative research, and for what purpose, should saturation be sought?‘When and how?’—at what stage in the research is saturation sought, and how can we assess if it has been achieved?However, despite having apparently attained something of the status of orthodoxy, saturation is defined within the literature in varying ways—or is sometimes undefined—and raises a number of problematic conceptual and methodological issues Dey . DrawingIn addressing these questions, we will explore the implications of different models of saturation—and the theoretical and methodological assumptions that underpin them—for the varying purposes saturation may serve across different qualitative approaches. In doing so, the paper will contribute to the small but growing literature that has critically examined the concept of saturation  saturation may refer to the extent to which pre-determined codes or themes are adequately represented in the data—rather like the idea of the categories being sufficiently replete with instances, or ‘examples’, of data, as suggested in the a priori thematic saturation model outlined above. Thus, in their attempt to establish an adequate sample size for saturation, Francis et al.  refer exindividual informants . In such studies, analysis tends to focus more on strands within individual accounts rather than on analytical themes; these strands are essentially continuous, whereas themes are essentially recurrent. Accordingly, Marshall and Long . In narrative research, a role for saturation is harder to discern. Rather than the sufficient development of theory, it might be seen to indicate the ‘completeness’ of a biographical account. However, one could question whether the point at which a participant’s story is interpreted as being ‘complete’—having presumably conveyed everything seen to be relevant to the focus of the study—is, in fact, usefully described by the concept of saturation, given the distance that this moves us away from the operationalization of saturation in broadly thematic approaches. This might, furthermore, lead us to ask whether there is the risk of saturation losing its coherence and utility if its potential conceptualization and uses are stretched too widely.The same issue is relevant with regard to a number of other, less obvious, purposes that have been proposed for saturation. For example, it has been claimed to demonstrate the trustworthiness of coding emergence of new codes or themes—might suggest it will be achieved at a later stage than in data saturation approaches . However, focusing on the emergence or otherwise of codes rather than on their theoretical development still points us towards saturation being achieved at a relatively early stage. Hennink et al.  highlighIn contrast to data saturation and inductive thematic saturation, the first model of saturation considered, theoretical saturation—as based on the grounded theory notion of determining when the properties of theoretical categories are adequately developed—indicates that the process of analysis is at a more advanced stage and at a higher level of theoretical generality. Accordingly, Zhao and Davey : p. 1178A key issue underlying the identification of saturation is the extent to which it is viewed as an event or a process. Commonly, saturation is referred to as a ‘point’ (e.g. Otmar et al. er or more insightful. The question will then be ‘how much saturation is enough?’, rather than ‘has saturation occurred?’On this incremental reading of saturation, the analysis does not suddenly become ‘rich’ or ‘insightful’ after that one additional interview, but presumably becomes richAfter the 10th interview, there were no new themes generated from the interviews. Therefore, it was deemed that the data collection had reached a saturation point. We continued data collection for two more interviews to ensure and confirm that there are no new themes emerging (Jassim and Whitford (Furthermore, a reluctance to rely on evidence of saturation sometimes indicates that saturation is being used in at best an unclear, or at worst an inconsistent or incoherent, fashion. For example, Hill et al. (Saturation was monitored continuously throughout recruitment. For completeness we chose to fully recruit to all participant groups to reduce the chance of missed themes.Similarly, Jackson et al. (Following analysis of eight sets of data, data saturation was established… however, two additional participants were recruited to ensure data saturation was achieved.Constantinou et al. (A desire to identify a specific point in time at which saturation is achieved seems often to give rise to a degree of uncertainty or equivocation. In a number of studies, saturation is claimed, but further data collection takes place in an apparent attempt to ‘confirm’ (Jassim and Whitford l et al. : p. 2, wn et al. : p. 1406u et al.  propose u et al. : p. 13. Whilst the above suggests ambivalence towards assessing the point at which saturation is achieved, others report having made the conscious decision to continue sampling beyond saturation, appearing to seek additional objective evidence to bolster their sampling decisions. For instance, in investigating staff and patient views on a stroke unit, Tutton et al. : p. 2063An a priori sample size of 30 to 40 was selected based on recommendations for qualitative studies of this nature… and the anticipated complexity and desired level of depth for our research questions.Fusch and Ness (Another indication of an ambivalent view taken on saturation is suggested by Mason’s  observatand Ness : p. 1409This tentative and equivocal commitment to saturation may reflect a practical response to the demands of funding bodies and ethics committees for a clear statement of sample size prior to starting a study (O’Reilly and Parker This paper has offered a critical reflection on the concept of saturation and its use in qualitative research, contributing to the small body of literature that has examined the complexities of the concept and its underlying assumptions. Drawing on recent examples of its use, saturation has been discussed in relation to three key sets of questions: What? Where and why? When and how?Extending previous literature that has highlighted the variability in the use of saturation (O’Reilly and Parker sole criterion of the adequacy of data collection and analysis (Charmaz Saturation’s apparent position as a ‘gold standard’ in assessing quality and its near universal application in qualitative research have been previously questioned (Guest et al.  Charmaz , or of t Charmaz : p. 186. Charmaz , may be Whilst arguing for flexibility in terms of the purpose and use of saturation, we also suggest that there must be some limit to this range of purposes. Some of the ways in which saturation has been operationalized, we would suggest, risk stretching or diluting its meaning to the point where it becomes too widely encompassing, thereby undermining its coherence and utility.When and how saturation may be judged to have been reached will differ depending on the type of study, as well as assumptions about whether it represents a distinct event or an ongoing process. The view of saturation as an event has been problematized by others (Strauss and Corbin In highlighting and examining these areas of complexity, this paper has extended previous discussions of saturation in the literature. Whilst consideration of the concept has led some commentators to argue for the need for qualitative researchers to provide a more thorough and transparent reporting of how they achieved saturation in their research, thus allowing readers to assess the validity of this claim Bowen , our arg